Question

Help please! (:

Integral Problem attached below.

Answer 1

Definition of improper integrals: split up the limits at points of discontinuity and add the integrals.

Answer 2

\[
\int _{-4}^{4}f(x)\;dx =\int _{-4}^{1}f(x)\;dx + \int _{1}^{4}f(x)\;dx = \int _{-4}^{1}7x\;dx + \int _{1}^{4}7\;dx
\]

Answer 3

how do i solve each integral?
do I derive 7x first or just plug in the values 1 and -4 find the difference then add it to the next integral?

Answer 4

by now you should know how to integrate.

Answer 5

Actually, one little detail I missed:
\[
\int _{-4}^{4}f(x)\;dx =\lim_{t\to 1^-}\int _{-4}^{t}f(x)\;dx + \lim_{t\to 1^+}\int _{t}^{4}f(x)\;dx
\]

Answer 6

However, in this case the limits are trivial because direct substitution and evaluation will work.

Answer 7

If you don't know the FTC, you can use basic geometric principles. The area for the \(x\ge1\) part is a rectangle, and the area for \(x<1\) is a trapezoid.

Answer 8

I'm still a little confused. on doing integrals, that's why im having a hard time

Answer 9

Do you know how to find anti-derivatives?

Answer 10

doing a derivative backwards. @wio