Question

Integration by substitution is related to what differentiation​ method? What type of integrand suggests using integration by​ substitution? Integration by substitution is related to what differentiation​ method? A. Integration by substitution is related to the exponential rule and logarithm rule. B. Integration by substitution is related to the power rule and quotient rule. C. Integration by substitution is related to the chain rule. D. Integration by substitution is related to the sum or difference rule.

Answer 1

Integration by substitution is an integration method meant to "undo" the chain rule for differentiation. This method is useful for some integrands containing compositions of functions.

For example, substitution is good for finding the antiderivative of 2x•cos(x^2). The quadratic function nested inside the cosine function suggests that substitution might be useful. And it is... the antiderivative is sin(x^2)+C

The answer is Choice C.

Answer 2

Answer:

C. Integration by substitution is related to the chain rule.

Step-by-step explanation:

In differentiation, when we want to differentiate a composite function, we use the chain rule.

In integration, to integrate a composite function, we use the integration by subtstitution method.

This means that the integration by substitution method is related to the chain rule of derivatives.

The correct answer is:

C. Integration by substitution is related to the chain rule.