U Substitution

Front

What is U Substitution in calculus?

Back

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

Front

When should you use U Substitution?

Back

Use U Substitution when the integral contains a composite function or when a part of the integrand can be simplified by substituting it with a single variable.

Front

Identify u in the integral ∫(5xsin(2x²))dx.

Back

u = 2x².

Front

What is the derivative of u = 2x²?

Back

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

Front

How do you change the limits of integration when using U Substitution?

Back

When using U Substitution, change the limits of integration to correspond to the new variable 'u' by substituting the original limits into the equation u = f(x).

Front

Evaluate the integral ∫(5xsin(2x²))dx using U Substitution.

Back

Let u = 2x², then du = 4xdx. The integral becomes (5/4)∫sin(u)du = -(5/4)cos(u) + C = -(5/4)cos(2x²) + C.

Front

What is the purpose of U Substitution?

Back

The purpose of U Substitution is to simplify complex integrals into a more manageable form, making it easier to find the antiderivative.

Front

What is the first step in U Substitution?

Back

The first step is to identify a part of the integrand to substitute with 'u' that will simplify the integral.

Front

Can U Substitution be used for definite integrals?

Back

Yes, U Substitution can be used for definite integrals, but you must change the limits of integration to match the new variable 'u'.

Front

What is the integral of sin(u)?

Back

The integral of sin(u) is -cos(u) + C.