U- Substitution Practice

Front

What is U-Substitution in integration?

Back

U-Substitution is a method used to simplify the process of integration by substituting a part of the integrand with a new variable 'u', making the integral easier to solve.

Front

When should you use U-Substitution?

Back

Use U-Substitution when the integrand is a composite function or when a function and its derivative appear in the integral.

Front

What is the formula for U-Substitution?

Back

If u = g(x), then du = g'(x)dx. The integral becomes ∫f(g(x))g'(x)dx = ∫f(u)du.

Front

How do you choose 'u' in U-Substitution?

Back

Choose 'u' to be a function inside another function or a part of the integrand that simplifies the integral when substituted.

Front

What is the derivative of u = 2x^2?

Back

du/dx = 4x, so du = 4xdx.

Front

What is the integral of sec^2(x) dx?

Back

The integral of sec^2(x) dx is tan(x) + C.

Front

What is the integral of (2 - x)^5 dx?

Back

The integral of (2 - x)^5 dx is -(1/6)(2 - x)^6 + C.

Front

What is the integral of x(x^2 + 7)^(1/3) dx?

Back

The integral of x(x^2 + 7)^(1/3) dx is (3/8)(x^2 + 7)^(4/3) + C.

Front

What is the integral of 5x sin(2x^2) dx using U-Substitution?

Back

Let u = 2x^2, then du = 4xdx, so the integral becomes (5/4)∫sin(u)du.

Front

What is the integral of (x^4 + 3)^3 dx?

Back

The integral of (x^4 + 3)^3 dx is (1/12)(x^4 + 3)^3 + C.