Home > Calculus > Formal Definition of the Definite Integral

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

Answer 1

Christopher Allers

#= 2/3#

#int_{-1)^0 dy qquad sqrt(y+1)#

this is simply the power rule ie #int du qquad u^n = n^{n+1}/(n+1)#

#=[2/3 (y+1)^(3/2)]_{-1)^0#

#=[2/3 (0+1)^(3/2)] - [2/3 (-1+1)^(3/2)] = 2/3#

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

Answer 2

Emily Ammerman

To find the definite integral of √(y + 1) dy from -1 to 0, you can use the substitution method. Let u = y + 1, then du = dy. The integral becomes ∫√u du. Evaluate the integral of √u with respect to u, and then replace u with y + 1. Finally, evaluate the expression at the upper and lower limits of integration, and subtract the result of the lower limit from the upper limit to find the definite integral value.

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.