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Integrals Class 12 Multiple Choice Test

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Integrals Class 12 (120701)


General Instruction:

1. There are 10 MCQ’s in the Test.

2. Passing %age is 50.

3. After time gets over, test will be submitted itself.

1 / 10

If \(F(x) = \int_{0}^{x} f(t) dt\), then according to the Fundamental Theorem of Calculus,  F'(x)  is equal to:

a) f(x)

b) F(x)

c) \(\int_{0}^{x} f'(t) dt\)

d) \(\frac{d}{dx} \int_{0}^{x} f(t) dt\)

2 / 10

Which of the following statements best describes integration as the inverse process of differentiation?

a) Integration finds the derivative of a function.

b) Integration finds the area under a curve.

c) Integration finds the original function given its derivative.

d) Integration finds the slope of a tangent line.

3 / 10

Which property of definite integrals allows us to split the integral of a sum into the sum of integrals?

a) Linearity

b) Associativity

c) Commutativity

d) Distributivity

4 / 10

Which technique is most appropriate for evaluating integrals involving rational functions?

a) Substitution

b) Partial fractions

c) Integration by parts

d) Trigonometric substitution

5 / 10

 Integration by parts is most useful when dealing with:

a) Exponential functions

b) Trigonometric functions

c) Polynomial functions

d) Rational functions

6 / 10

The integral of \( \sin(x) \cos(x)\) with respect to x is:

a) \(\frac{1}{2}\sin^2(x) + C \)

b) \(-\frac{1}{2}\cos^2(x) + C\)

c) \( -\frac{1}{2}\sin^2(x) + C\)

d) \(\frac{1}{2}\cos^2(x) + C\)

7 / 10

If f(x) is an odd function, then the integral \(\int_{-a}^{a} f(x) dx\) is equal to:

a) 0

b) \( 2\int_{0}^{a} f(x) dx\)

c) \( \int_{-a}^{0} f(x) dx\)

d) \( \int_{0}^{a} f(x) dx\)

8 / 10

The definite integral of \(e^x \) from 0 to 1 is equal to:

a) \(e^{-1}\)

b) \(e + 1\)

c) \(e^2 – 1\)

d) \( e^2 + 1\)

9 / 10

The integral \( \int \frac{1}{1+x^2} dx\) can be evaluated using:

a) Trigonometric substitution

b) Partial fractions

c) Integration by parts

d) Substitution

10 / 10

Which of the following is true regarding definite integrals?

a) They can be negative.

b) They always evaluate to zero.

c) They represent the area under the curve.

d) They only apply to continuous functions.

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