Someone check if my answer is correct pls? Calculus: FInd the area of the region between y=x^2 and =-5...?

Question

Problem is: Find the area of the region between y=x^2 and y=-5 for x in (-5,5)

Choices of answers are: a. 400/3 b. 5 c. 1200 d. 24/3 e. 400

I got 400/3, but not sure if it's correct, someone please check for me? Thanks!

Answer 1

Your answer is correct!

∫(x²-(-5)) dx = x³/3 + 5x
for x in (-5,5) that makes

125/3 + 25 +125/3 + 25 =
400/3

Answer 2

You have to calculate the integral of(x^2+5) for x between -5 and 5which ould be
2 Int(x^2+5)dx between 0 and 5 as the integrand is even
=2(5^3/3+25)=400/3 so you are right

Answer 3

int(-5 to 5) x^2 + 5 dx
=x^3 / 3 +5x eval from -5 to 5
=2(125/3 + 25)
=50 + 250 / 3
=400/3

nice work!

:)