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

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

The integral of \(\frac{1}{x^2}\) with respect to x is:

a) \(\ln|x| + C\)

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

c) \(\frac{1}{x} + C\)

d) \(-\ln|x| + C\)

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

a) Trigonometric substitution

b) Partial fractions

c) Integration by parts

d) Substitution

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

a) Substitution

b) Partial fractions

c) Integration by parts

d) Trigonometric substitution

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.

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

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

Which method is typically used to evaluate integrals of products of functions?

a) Substitution

b) Partial fractions

c) Integration by parts

d) Trigonometric substitution

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