The process of finding the antiderivative is called ___.

Integration

True or False: Integration is the inverse process of differentiation.

True. Integration reverses the effect of differentiation, allowing us to recover functions from their derivatives.

The constant 'c' in the integration formula is referred to as the ___.

Constant of integration

In the context of integration, if g'(x) = f(x), then the integral of f(x) is expressed as ___.

G(x) + c

The fundamental theorem of calculus states that if F is an antiderivative of f on an interval [a, b], then the integral from a to b of f(x)dx is equal to ___.

F(b) - F(a)

Fill in the blank: The integral of sin x dx is ___.

−cos x + c

What is the geometrical significance of integration?

Integration gives the area under the curve of a bounded function.

True or False: The integral of a constant k with respect to x is kx + c.

True. The integral of a constant k is k multiplied by the variable of integration, plus the constant of integration.

The method of substitution in integration is typically used to simplify integrals by substituting ___.

A continuously differentiable function for the variable.

In integration by parts, if u and v are differentiable functions, the integral of u dv is equal to ___.

U v - ∫v du

Fill in the blank: The integral of (1/(ax + b)) dx is ___.

(1/a) * log |ax + b| + c

What does the method of partial fractions achieve in the integration of rational functions?

It allows the decomposition of a rational function into simpler fractions that can be integrated individually.

True or False: The integral of e^x dx is e^x + c.

True. The integral of e^x is itself plus the constant of integration.

Fill in the blank: The integral of sec x tan x dx is ___.

Sec x + c

In the context of integration, the term 'integrand' refers to ___.

The function that is being integrated.