Home > Calculus > Integrals of Polynomial functions

How do you integrate #int (1+3t)t^2dt#?

Answer 1

Ezekiel Alexander

The answer is #=t^3/3+(3t^4)/4+C#

We use, #intx^ndx=x^(n+1)/(n+1)+C (x!=-1)#

So,

#int(1+3t)t^2dt=int (t^2+3t^3)dt#

#=intt^2dt+3intt^3dt#

#=t^3/3+3t^4/4+C#

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

Answer 2

Aurora Alvarado

To integrate the expression ∫ (1 + 3t) * t^2 dt, you can expand the expression inside the integral and then integrate each term separately. Here's how you can do it:

∫ (1 + 3t) * t^2 dt = ∫ (t^2 + 3t^3) dt = ∫ t^2 dt + ∫ 3t^3 dt

Now, integrate each term: ∫ t^2 dt = (1/3) * t^3 + C1 ∫ 3t^3 dt = (3/4) * t^4 + C2

Combine the results: = (1/3) * t^3 + (3/4) * t^4 + C

Where C is the constant of integration.

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.