Definite Integrals Exercises

Answer

Answer

We can combine the integrals to get

Then pull out the constant to get

Since this must equal 48,

Answer

Split up the integral and pull out the constants:

We can find  by looking at a graph. The region between x and the x-axis on [0, 3] is a triangle with base 3 and height 3, so its area is 4.5.

Since this must equal 39,

.

Answer

Split up the integral, then evaluate the integral of the constant (don't be fooled by the order of the limits):

Since we know this whole mess must equal 34,

Switch the limits and switch the signs, then use the fact that f is even:

We conclude that .

Answer

Split up the integral, pull out the constant, and evaluate the integral of 4:

Since this needs to equal 26, we'll clean some things up.

Now switch the limits and switch the sign:

Split up the integral:

Since f is odd, its integral from -2 to 2 is zero, so