Question

Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F.

f(x) = 5x^4 − 4x^5, F(0) = 6

Answer 1

so you take the integral (antiderivative) but you'll get a constant. Sub zeros in for all your x's and set you y to 6 and you'll be able to solve the constant

Answer 2

Your familiar with the power rule for antiderivatives?

Answer 3

no, we literally just started them.

Answer 4

have you covered derivatives?

Answer 5

yes

Answer 6

ok so the power rule states:
\[\huge{\frac{d}{dx}x^n=nx^{n-1}}\]
so you drop the exponent in front and reduce the exponent by one

Answer 7

antiderivative would be just the opposite. For the antiderivative you first increase the exponent by one and then 'divide' by that new exponent

Answer 8

ohh okay!

Answer 9

\[\huge{\int\limits_{}^{}x^n=\frac{x^{n+1}}{n+1}}\]

Answer 10

You'll do that for each term, and introduce the c as a constant of integration

Answer 11

thanks!