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

St. Britto Hr. Sec. School - Madurai

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

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

Integrate the following with respect to x.
xe^−x

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

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

Integrate the following with rexpect to x
\(\frac { { a }^{ x }-{ e }^{ xlogb } }{ { e }^{ xloga }{ b }^{ x } } \)

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

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

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

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

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sqrt { 1+cosx } dx } \)

Evaluate the following using properties of definite integrals:
\(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }\theta } d\theta \)

Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)

Integrate the following with respect to x
\(\frac { 6x+7 }{ \sqrt { { 3x }^{ 2 }+7x-1 } } \)

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { sin }^{ 7 }x }{ { sin }^{ 7 }x+{ cos }^{ 7 }x } dx } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }+6x+13 } } \)

Integrate the following with respect to x
\(\frac { 1 }{ { 9-16x }^{ 2 } } \)

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

Evaluate the following:
\(\int _{ 1 }^{ 4 }{ f(x) } dx\) where f(x) = \(\begin{cases} 4x+3, \\ 3x+5, \end{cases}\begin{matrix} 1 & \le & x \\ 2 & \le & x \end{matrix}\begin{matrix} \le & 2 \\ \le & 4 \end{matrix}\)

Integrate the following with respect to x.

\({ \left( { 9x }^{ 2 }-\frac { 4 }{ { x }^{ 2 } } \right) }^{ 2 }\)

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)

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

Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ \frac { 1 }{ 4 } }{ \sqrt { 1-4 }\ dx } \)

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

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

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

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

St. Britto Hr. Sec. School - Madurai

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

Part - A

Generic 2 - Answer All Question

Integrate the following with respect to x. xe−x

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

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

Integrate the following with rexpect to x \(\frac { { a }^{ x }-{ e }^{ xlogb } }{ { e }^{ xloga }{ b }^{ x } } \)

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

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

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

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

Using second fundamental theorem, evaluate the following: \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sqrt { 1+cosx } dx } \)

Evaluate the following using properties of definite integrals: \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }\theta } d\theta \)

Integrate the following with respect to x. \(\sqrt { 3x+5 } \)

Integrate the following with respect to x \(\frac { 6x+7 }{ \sqrt { { 3x }^{ 2 }+7x-1 } } \)

Evaluate the following using properties of definite integrals: \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { sin }^{ 7 }x }{ { sin }^{ 7 }x+{ cos }^{ 7 }x } dx } \)

Integrate the following with respect to x \(\frac { 1 }{ \sqrt { { x }^{ 2 }+6x+13 } } \)

Integrate the following with respect to x \(\frac { 1 }{ { 9-16x }^{ 2 } } \)

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

Evaluate the following: \(\int _{ 1 }^{ 4 }{ f(x) } dx\) where f(x) = \(\begin{cases} 4x+3, \\ 3x+5, \end{cases}\begin{matrix} 1 & \le & x \\ 2 & \le & x \end{matrix}\begin{matrix} \le & 2 \\ \le & 4 \end{matrix}\)

Integrate the following with respect to x. \({ \left( { 9x }^{ 2 }-\frac { 4 }{ { x }^{ 2 } } \right) }^{ 2 }\)

Evaluate the following integrals as the limit of the sum: \(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)

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

Evaluate the following integrals: \(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)

Using second fundamental theorem, evaluate the following: \(\int _{ 0 }^{ \frac { 1 }{ 4 } }{ \sqrt { 1-4 }\ dx } \)

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

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

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

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Tamilnadu Stateboardszs - Class

Integrate the following with respect to x.
xe^−x

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

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

Integrate the following with rexpect to x
\(\frac { { a }^{ x }-{ e }^{ xlogb } }{ { e }^{ xloga }{ b }^{ x } } \)

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

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

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

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

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sqrt { 1+cosx } dx } \)

Evaluate the following using properties of definite integrals:
\(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }\theta } d\theta \)

Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)

Integrate the following with respect to x
\(\frac { 6x+7 }{ \sqrt { { 3x }^{ 2 }+7x-1 } } \)

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { sin }^{ 7 }x }{ { sin }^{ 7 }x+{ cos }^{ 7 }x } dx } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }+6x+13 } } \)

Integrate the following with respect to x
\(\frac { 1 }{ { 9-16x }^{ 2 } } \)

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

Evaluate the following:
\(\int _{ 1 }^{ 4 }{ f(x) } dx\) where f(x) = \(\begin{cases} 4x+3, \\ 3x+5, \end{cases}\begin{matrix} 1 & \le & x \\ 2 & \le & x \end{matrix}\begin{matrix} \le & 2 \\ \le & 4 \end{matrix}\)

Integrate the following with respect to x.

\({ \left( { 9x }^{ 2 }-\frac { 4 }{ { x }^{ 2 } } \right) }^{ 2 }\)

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)

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

Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ \frac { 1 }{ 4 } }{ \sqrt { 1-4 }\ dx } \)

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

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

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