Antiderivative Practice

Front

What is the antiderivative of -sin(x)?

Back

The antiderivative of -sin(x) is cos(x) + C.

Front

Integrate the function x^(1/2).

Back

The antiderivative is (2/3)x^(3/2) + C.

Front

What does '+C' represent in the context of antiderivatives?

Back

'+C' represents an unknown constant.

Front

Back

Front

If f '(x) = x^(-2) - x^(-3) + 5x^(-6), what is f(x)?

Back

f(x) = -x^(-1) + ½x^(-2) - x^(-5) + C.

Front

What is the general formula for finding the antiderivative of x^n?

Back

The antiderivative of x^n is (1/(n+1))x^(n+1) + C, where n ≠ -1.

Front

What is the antiderivative of cos(x)?

Back

The antiderivative of cos(x) is sin(x) + C.

Front

What is the integral of a constant k?

Back

The integral of a constant k is kx + C.

Front

How do you integrate a polynomial function?

Back

To integrate a polynomial function, apply the power rule: increase the exponent by 1 and divide by the new exponent.

Front

What is the antiderivative of e^x?

Back

The antiderivative of e^x is e^x + C.