Home > Calculus > Definite and indefinite integrals

Evaluate the integral of (x√x-3dx)?

Answer 1

Charles Arocha

the answer
#intx^(3/2)-3*dx=[2/5*x^(5/2)-3x]+c#

if your integral was #intxsqrtx-3dx#

rewrite it #intx^(3/2)-3*dx#

We will now assess it.

#intx^(3/2)-3*dx=[2/5*x^(5/2)-3x]+c#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Paisley Johnson

# 2/5(x-3)^(3/2)*(x+2)+C#.

If the integral is, #I=intxsqrt(x-3)dx#, then, we have,

#I=int{(x-3)+3}sqrt(x-3)dx#,

#=int{(x-3)sqrt(x-3)+3sqrt(x-3)}dx#,

#=int{(x-3)^(3/2)+3(x-3)^(1/2)}dx#,

#=(x-3)^(3/2+1)/(3/2+1)+3*(x-3)^(1/2+1)/(1/2+1)#,

#=2/5(x-3)^(5/2)+3*2/3(x-3)^(3/2)#,

#=2/5(x-3)^(3/2){(x-3)+5}#.

#:. I=intxsqrt(x-3)dx=2/5(x-3)^(3/2)*(x+2)+C#.

Share the Love of Mathematics!

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.