What is the integral?

Question

Given that₀¹ 15xx²+4 dx = 255 - 40, what is ₁⁰ 15uu²+4 du?

Given that integral [0,1] 15x (sqrt x²)+4 dx = 25(sqrt 5) - 40, what is integral [1,0] 15u(sqrt u²+4) du?

*I do not know if I wrote the integrals correctly on the written out form but for the first integral 0 is on the bottom and 1 is on top, and for the second integral, 1 is on the bottom and 0 is on top.

Answer 1

at first it appears the answer you want is 40-25sqr5 Just switch the signs.

that assumes 25sqr5 -40 is correct as the integral of 15xsqr(x^2+4)

That is the solution SnapXam, an online integral calculator has

integration tables on wikipedia also have the same integral

for sqr(x+a) =(1/3)(x^2+a)^(3/2)

when a =4, and multiply by 15 you get the same answer

check the integral by taking the derivative and see if it is 15xsqr(x^2+4)

[5(x^2+4)^(3/2)]'

= (3/2)(5)(x^2+4)^(1/2)(2x

= 15x(x^2+4)^(1/2)

evalute the integral between 0 and 1

5(0^2 +4)^(3/2) - 5(1^2 +4)^(3/2

=5[4^(3/2) - 5^(3/2)]

=5(8 -5sqr5)

= 40 -25sqr5 which is just switching the signs of 25sq5-40

you probably have a typo when you typed 15x(sqr x^2)+4 dx

but if you somehow really meant that then

the integral of 15x(sqrx^2)+4 dx

= the integral of 15x(x) +4 dx

= 5x +4t

evaluated from 0 to 1 is 9

evaluated from 1 to 0 is -9, Again just change the sign