Integration Review

Front

What is the integral of a constant function c over the interval [a, b]?

Back

The integral is c(b - a).

Front

What is the Fundamental Theorem of Calculus?

Back

It states that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

What is the power rule for integration?

Back

The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, for n ≠ -1.

Front

What is the integral of sin(x)?

Back

The integral is -cos(x) + C.

Front

What is the integral of e^x?

Back

The integral is e^x + C.

Front

What is the integration by parts formula?

Back

∫u dv = uv - ∫v du.

Front

What is the integral of cos(kx)?

Back

The integral is (1/k)sin(kx) + C.

Front

What is the integral of a polynomial function?

Back

Integrate term by term using the power rule.

Front

What is the area under a curve represented by an integral?

Back

The area under the curve f(x) from a to b is given by ∫_a^b f(x)dx.

Front

What is the integral of 1/x?

Back

The integral is ln|x| + C.