Home > Calculus > Formal Definition of the Definite Integral

How do you find the definite integral of #sqrt(y+1)dy# from #[0,3]#?

Answer 1

Elijah Abram

I found: #14/3#

We can try this:

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

Answer 2

Luke Alvarez

To find the definite integral of √(y + 1) dy from 0 to 3, you first need to find the antiderivative of √(y + 1) with respect to y, and then evaluate it at the upper limit (3) and subtract the value at the lower limit (0). The antiderivative of √(y + 1) with respect to y is (2/3)(y + 1)^(3/2). Therefore, the definite integral from 0 to 3 is [(2/3)(3 + 1)^(3/2)] - [(2/3)*(0 + 1)^(3/2)]. Simplify these expressions to get the final answer.

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.