U-Substitution

Front

What is U-Substitution in calculus?

Back

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

Front

What is the purpose of choosing 'u' in U-Substitution?

Back

The purpose of choosing 'u' is to simplify the integral into a more manageable form, often by selecting a function whose derivative is also present in the integral.

Front

What does 'du' represent in U-Substitution?

Back

'du' represents the differential of 'u', which is the derivative of 'u' with respect to 'x' multiplied by 'dx'.

Front

How do you find 'du' when using U-Substitution?

Back

To find 'du', differentiate 'u' with respect to 'x' and multiply by 'dx': du = (du/dx)dx.

Front

What is the first step in applying U-Substitution?

Back

The first step is to identify a suitable substitution for 'u' that simplifies the integral.

Front

When should you revert back to the original variable after integration?

Back

You should revert back to the original variable after performing the integration and before finalizing the answer.

Front

What is an example of a function suitable for U-Substitution?

Back

An example is the integral of sin(x)cos(x)dx, where you can let u = sin(x).

Front

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

Back

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

Front

If u = sin(x), what is du?

Back

If u = sin(x), then du = cos(x)dx.

Front

What is the integral of tan(x)sec(x)dx?

Back

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