12th Business Maths Monthly Test - 2 ( Integral Calculus – I )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Integral Calculus – I )-Aug 2020

Time : 2.30 Hours

Part - A

Generic 2 - Answer All Question

Evaluate the following integrals:
ഽ\(\sqrt { 2{ x }^{ 2 }-3 } \) dx

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ log\left( \frac { 1 }{ x } -1 \right) dx } \)

Evaluate the following integrals:
ഽ\(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

Integrate the following with respect to x.
\(\int \frac { { x }^{ 3 } }{ x+2 } dx\)

Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ 2 }{ \frac { x-1 }{ { x }^{ 2 } } dx } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x.
\(\frac { 2x+5 }{ { x }^{ 2 }+5x-7 } \)

Evaluate the following using properties of definite integrals:
\(\int _{ -1 }^{ 1 }{ log\left( \frac { 2-x }{ 2+x } \right) } dx\)

Integrate the following with respect to x.
\(\frac { { e }^{ 3x }-{ e }^{ -3x } }{ { e }^{ x } } \)

Integrate the following with respect to x
\(\frac { 1 }{ x+\sqrt { { x }^{ 2 }-1 } } \)

Evaluate the following:
\(f(x)=\begin{cases}cx, \quad 0<x<1 \\ 0, \quad otherwise \end{cases}\) find 'c' if \(\int ^1 _0 f(x)\ dx\)

Integrate the following with respect to x.
xⁿlog x

If f(x) = \(f(x)=\begin{cases} { x }^{ 2 }{ e }^{ -2x },x\ge 0 \\ 0,otherwise \end{cases}\), then evaluate \(\int _{ 0 }^{ \infty }{ f(x) } dx\)

Integrate the following with respect to x.

\(\sqrt{x}\)(x³− 2x + 3)

Integrate the following with respect x
\(\frac { 3x+2 }{ \left( x-2 \right) \left( x-3 \right) } \)

Integrate the following with respect to x.
\(\frac { { 4x }^{ 2 }+2x+6 }{ { \left( x+1 \right) }^{ 2 }\left( x-3 \right) } \)

Integrate the following with respect to x
\(\sqrt { { x }^{ 2 }-2 } \)

Integrate the following with respect to x.
\(\left[ 1-\frac { 1 }{ { x }^{ 2 } } \right] { e }^{ \left( x+\frac { 1 }{ x } \right) }\)

Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { 9x }^{ 2 }-7 } } \)

Integrate the following with respect to x.
\(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

Integrate the following with respect to x
\(\frac { 1 }{ { x }^{ 2 }+3x+2 } \)

Integrate the following with respect to x.
\(\frac { 1 }{ x({ x }^{ 2 }+1) } \)

Integrate the following with respect to x.
(e^x +1)² e^x

If f(x) = 8x³ − 2x and f (2)= 8, then find f (x)

Evaluate the following integrals:
ഽ\(\frac { 1 }{ \sqrt { x+2 } -\sqrt { x+3 } } \)dx

Integrate the following with respect to x.
log x

Integrate the following with respect to x.
\({ e }^{ 3x }\left[ \frac { 3x-1 }{ { 9x }^{ 2 } } \right] \)

Evaluate the following integrals:
\(\int _{ -1 }^{ 1 }{ { x }^{ 2 }{ e }^{ -2x } } dx\)

Evaluate the following integrals:
ഽ log(x −\(\sqrt { { x }^{ 2 }-1 } \)) dx

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12th Business Maths Monthly Test - 2 ( Integral Calculus – I )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Integral Calculus – I )-Aug 2020

Part - A

Generic 2 - Answer All Question

Evaluate the following integrals: ഽ\(\sqrt { 2{ x }^{ 2 }-3 } \) dx

Evaluate the following using properties of definite integrals: \(\int _{ 0 }^{ 1 }{ log\left( \frac { 1 }{ x } -1 \right) dx } \)

Evaluate the following integrals: ഽ\(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

Integrate the following with respect to x. \(\int \frac { { x }^{ 3 } }{ x+2 } dx\)

Using second fundamental theorem, evaluate the following: \(\int _{ 1 }^{ 2 }{ \frac { x-1 }{ { x }^{ 2 } } dx } \)

Using second fundamental theorem, evaluate the following: \(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x. \(\frac { 2x+5 }{ { x }^{ 2 }+5x-7 } \)

Evaluate the following using properties of definite integrals: \(\int _{ -1 }^{ 1 }{ log\left( \frac { 2-x }{ 2+x } \right) } dx\)

Integrate the following with respect to x. \(\frac { { e }^{ 3x }-{ e }^{ -3x } }{ { e }^{ x } } \)

Integrate the following with respect to x \(\frac { 1 }{ x+\sqrt { { x }^{ 2 }-1 } } \)

Evaluate the following: \(f(x)=\begin{cases}cx, \quad 0<x<1 \\ 0, \quad otherwise \end{cases}\) find 'c' if \(\int ^1 _0 f(x)\ dx\)

Integrate the following with respect to x. xn log x

If f(x) = \(f(x)=\begin{cases} { x }^{ 2 }{ e }^{ -2x },x\ge 0 \\ 0,otherwise \end{cases}\), then evaluate \(\int _{ 0 }^{ \infty }{ f(x) } dx\)

Integrate the following with respect to x. \(\sqrt{x}\)(x3 − 2x + 3)

Integrate the following with respect x \(\frac { 3x+2 }{ \left( x-2 \right) \left( x-3 \right) } \)

Integrate the following with respect to x. \(\frac { { 4x }^{ 2 }+2x+6 }{ { \left( x+1 \right) }^{ 2 }\left( x-3 \right) } \)

Integrate the following with respect to x \(\sqrt { { x }^{ 2 }-2 } \)

Integrate the following with respect to x. \(\left[ 1-\frac { 1 }{ { x }^{ 2 } } \right] { e }^{ \left( x+\frac { 1 }{ x } \right) }\)

Evaluate the following using properties of definite integrals: \(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)

Integrate the following with respect to x \(\frac { 1 }{ \sqrt { { 9x }^{ 2 }-7 } } \)

Integrate the following with respect to x. \(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

Integrate the following with respect to x \(\frac { 1 }{ { x }^{ 2 }+3x+2 } \)

Integrate the following with respect to x. \(\frac { 1 }{ x({ x }^{ 2 }+1) } \)

Integrate the following with respect to x. (ex +1)2 ex

If f(x) = 8x3 − 2x and f (2)= 8, then find f (x)

Evaluate the following integrals: ഽ\(\frac { 1 }{ \sqrt { x+2 } -\sqrt { x+3 } } \)dx

Integrate the following with respect to x. log x

Integrate the following with respect to x. \({ e }^{ 3x }\left[ \frac { 3x-1 }{ { 9x }^{ 2 } } \right] \)

Evaluate the following integrals: \(\int _{ -1 }^{ 1 }{ { x }^{ 2 }{ e }^{ -2x } } dx\)

Evaluate the following integrals: ഽ log(x −\(\sqrt { { x }^{ 2 }-1 } \)) dx

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Evaluate the following integrals:
ഽ\(\sqrt { 2{ x }^{ 2 }-3 } \) dx

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ log\left( \frac { 1 }{ x } -1 \right) dx } \)

Evaluate the following integrals:
ഽ\(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

Integrate the following with respect to x.
\(\int \frac { { x }^{ 3 } }{ x+2 } dx\)

Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ 2 }{ \frac { x-1 }{ { x }^{ 2 } } dx } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x.
\(\frac { 2x+5 }{ { x }^{ 2 }+5x-7 } \)

Evaluate the following using properties of definite integrals:
\(\int _{ -1 }^{ 1 }{ log\left( \frac { 2-x }{ 2+x } \right) } dx\)

Integrate the following with respect to x.
\(\frac { { e }^{ 3x }-{ e }^{ -3x } }{ { e }^{ x } } \)

Integrate the following with respect to x
\(\frac { 1 }{ x+\sqrt { { x }^{ 2 }-1 } } \)

Evaluate the following:
\(f(x)=\begin{cases}cx, \quad 0<x<1 \\ 0, \quad otherwise \end{cases}\) find 'c' if \(\int ^1 _0 f(x)\ dx\)

Integrate the following with respect to x.
xⁿlog x

Integrate the following with respect to x.

\(\sqrt{x}\)(x³− 2x + 3)

Integrate the following with respect x
\(\frac { 3x+2 }{ \left( x-2 \right) \left( x-3 \right) } \)

Integrate the following with respect to x.
\(\frac { { 4x }^{ 2 }+2x+6 }{ { \left( x+1 \right) }^{ 2 }\left( x-3 \right) } \)

Integrate the following with respect to x
\(\sqrt { { x }^{ 2 }-2 } \)

Integrate the following with respect to x.
\(\left[ 1-\frac { 1 }{ { x }^{ 2 } } \right] { e }^{ \left( x+\frac { 1 }{ x } \right) }\)

Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { 9x }^{ 2 }-7 } } \)

Integrate the following with respect to x.
\(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

Integrate the following with respect to x
\(\frac { 1 }{ { x }^{ 2 }+3x+2 } \)

Integrate the following with respect to x.
\(\frac { 1 }{ x({ x }^{ 2 }+1) } \)

Integrate the following with respect to x.
(e^x +1)² e^x

If f(x) = 8x³ − 2x and f (2)= 8, then find f (x)

Evaluate the following integrals:
ഽ\(\frac { 1 }{ \sqrt { x+2 } -\sqrt { x+3 } } \)dx

Integrate the following with respect to x.
log x

Integrate the following with respect to x.
\({ e }^{ 3x }\left[ \frac { 3x-1 }{ { 9x }^{ 2 } } \right] \)

Evaluate the following integrals:
\(\int _{ -1 }^{ 1 }{ { x }^{ 2 }{ e }^{ -2x } } dx\)

Evaluate the following integrals:
ഽ log(x −\(\sqrt { { x }^{ 2 }-1 } \)) dx