Question

Find the area under the curve of the function y=x^3 + x^2 from x=0 to x=1

Answer 1

Easiest to integrate separately and then add. Are you able to integrate x^3?

Answer 2

As you probably know, integration is the opposite of differentiation, so the anti-derivative of x^3 is (1/4)x^4 because when taking its derivative you get x^3. With me so far?

Answer 3

The anti-derivative of x^2 is (1/3)x^3.

Answer 4

\[so, \int\limits_{0}^{1} (x ^{3} + x ^{2}) dx = (1/4)x ^{4} + (1/3)^{3} evaluated \between 0 and 1.\]

Answer 5

so,∫ 0 1 (x 3 +x 2 )dx=(1/4)x 4 +(1/3)x^ 3 evaluated≬0and1.

Answer 6

Sorry, ther was supposed to be an x between the (1/3) and the 3 exponent.

Answer 7

So, you should come up with 1/12.

Answer 8

7/12.