12th Business Maths Weekly Test - 3 ( Integral Calculus – I )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Integral Calculus – I )-Aug 2020

Time : 1.15 Hours

Part - A

Generic 2 - Answer All Question

Evaluate the following integrals:
ഽ(x +1)² log x dx

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

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.
\(\sqrt { 3x+5 } \)

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

Integrate the following with respect to x.
x³e^3x

Evaluate the following integrals:
ഽ\(\sqrt { 9{ x }^{ 2 }+12x+3 } \) dx

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

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

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

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

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

If f(x) = x + b, f (1)= 5 and f (2) = 13, then find f (x)

Integrate the following with respect to x.
(4x + 2) \(\sqrt { { x }^{ 2 }+x+1 } \)

Evaluate the following:
\(\int _{ 0 }^{ 2 }{ f(x) } dx\) where \( \cases{ 3-2x-x^2, \quad x\le 1 \\ x^2 +2x -3, \quad 1<x<2}\)

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12th Business Maths Weekly Test - 3 ( Integral Calculus – I )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Integral Calculus – I )-Aug 2020

Part - A

Generic 2 - Answer All Question

Evaluate the following integrals: ഽ(x +1)2 log x dx

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

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. \(\sqrt { 3x+5 } \)

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

Integrate the following with respect to x. x3e3x

Evaluate the following integrals: ഽ\(\sqrt { 9{ x }^{ 2 }+12x+3 } \) dx

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

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

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

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

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

If f(x) = x + b, f (1)= 5 and f (2) = 13, then find f (x)

Integrate the following with respect to x. (4x + 2) \(\sqrt { { x }^{ 2 }+x+1 } \)

Evaluate the following: \(\int _{ 0 }^{ 2 }{ f(x) } dx\) where \( \cases{ 3-2x-x^2, \quad x\le 1 \\ x^2 +2x -3, \quad 1<x<2}\)

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Tamilnadu Stateboardszs - Class

Evaluate the following integrals:
ഽ(x +1)² log x dx

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

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.
\(\sqrt { 3x+5 } \)

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

Integrate the following with respect to x.
x³e^3x

Evaluate the following integrals:
ഽ\(\sqrt { 9{ x }^{ 2 }+12x+3 } \) dx

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

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

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

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

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

Integrate the following with respect to x.
(4x + 2) \(\sqrt { { x }^{ 2 }+x+1 } \)

Evaluate the following:
\(\int _{ 0 }^{ 2 }{ f(x) } dx\) where \( \cases{ 3-2x-x^2, \quad x\le 1 \\ x^2 +2x -3, \quad 1<x<2}\)