Question

$\int\limits^3_1 x³ dx ,Obtain the given integrals as the limit of a sum.$

Answer 1

HELLO DEAR,

YOUR QUESTIONS IS--------------$\sf{\int\limits^3_1 x^3dx}$,Obtain the given integrals as the limit of a sum.

$\sf{I =\int\limits^3_1 x^3\,dx}$

therefore, I = $\sf{[{x^{3 + 1}\over(1 + 3)}]^3_1}$

I = $\sf{[x^4/4]^3_1}$

I = (3)⁴/4 - (1)⁴/4

I = 81/4 - 1/4

I = (81 - 1)/4

I = 80/4 = 20

I = 20

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

we have to get the value of $\int\limits^3_1{x^3}\,dx$

we know, $\int{x^n}\,dx=\left[\frac{x^{n+1}}{n+1}\right]+C$

here,
$\int\limits^3_1{x^3}\,dx\\\\\\=\left[\frac{x^4}{4}\right]^3_1\\\\\\=\frac{1}{4}\left(3^4-1^4\right)\\\\\\=\frac{1}{4}(81-1)=20$