Integration by Substitution Lesson

5 Slides • 4 Questions

1

Integrals using substitution

2

Open Ended

If u= $x^2$ and f(u)= $u^3$ then find $\int_{ }^{ }f\left(u\right)du$ as a function of u.

Type response here

3

Open Ended

If u= $x^2$ and f(u)= $u^3$ then find $\int_{ }^{ }f\left(u\right)du\$ as a function of x this time.

Type response here

4

Multiple Choice

If u=x^2, what does du = ?

1

du=dx

2

du=2x dx

3

$\frac{du}{dx}=2x$

4

du= $\frac{1}{3}x^{3\ }$

5

du= $x^3+c$

5

Open Ended

$\int_{ }^{ }f\left(x\right)dx\ \ \ \ \ \ \int_{ }^{ }f\left(u\right)du\ \ \ \ \ \ \int_{ }^{ }f\left(x\right)du\ \ \ \ \ \int_{ }^{ }f\left(u\right)dx$

Let f(x)=x3+1 and u=x2, which of these are equivalent?

Type response here

6

Integration using substitution

7

Identify an "inside" function as your u-function

Then find the derivative of that u-function in terms of x.

8

Now you can simplify and integrate

Substitute the u-function and the value of du to make the integrand easier to integrate, then integrate and finally substitute back to have an equation in x.

9

https://youtu.be/b76wePnIBdU go to this link!

Integrals using substitution

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