Question

its an integration question ​

Answer 1

Answer:

The answer of given integral is 66.

Step-by-step explanation:

First, open the parenthesis:

$\int\limits^4_2 ({3x^2+5}) \, dx$

$\int\limits^4_2 {3x^2} dx+ \int\limits^4_2 {5} dx$

Write above equation as:

$3 \int\limits^4_2 {x^2} dx+ \int\limits^4_2 {5} dx$

As by integrating above becomes:

$3(\frac{x^3}{3})|^{4}_{2}+5(x)|^{4}_{2}$

After cancellation:

$x^3|^{4}_{2}+5x|^{4}_{2}$

As it is known :

$\int\limits^a_b {f(x)} \, dx= g(x)|^{a}_{b} = g(a)-g(b)$

So,

$(4^3-2^3)+5(4-2)$

$(64-8)+5(2)$

$56+10$

$66$