Integrals using substitution

Integrals using substitution

Open Ended

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

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.  

Multiple Choice

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

• du=dx

• du=2x dx

• $\frac{du}{dx}=2x$

• du= $\frac{1}{3}x^{3\ }$

• du= $x^3+c$

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?

Integration using substitution

Identify an "inside" function as your u-function

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

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.

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