How do you find the definite integral of (3x^3 +7) dx from [1, 5]?

1 Answer
Jun 26, 2016

496

Explanation:

color(red)(|bar(ul(color(white)(a/a)color(black)(int_a^bf(x)dx=[F(x)]_a^b=F(b)-F(a))color(white)(a/a)|)))

Integrate each term using the color(blue)"power rule"

int(ax^n)dx=a/(n+1)x^(n+1)

rArrint_1^5(3x^3+7)dx=[3/4x^4+7x]_1^5

=(3/4(5)^4+7(5))-(3/4(1)^4+7(1))

=1875/4+35-3/4-7=1872/4+28=496