Thread: Integrals and Sigma

Hello I need help with 2 problems.

The first is

Code:

F(x)= Integral from sqrt(x) to 2  (tan(t)/t^2) dt     Find F'(x)

The second is

Code:

Find the actual area under the curve f(x)=2x^2 on the interval [0,3]. Use right hand endpoints and the formula
Area = lim n→ ∞   n Σ i=1    f(x^*i) delta(x)

Here is an image of the equations

For the first part, I would perform the following transformation:



Let and changing the bounds gives



Then you can make use of the Second Fundamental Theorem of Calculus.

For the second, you have been given a formula to use. Where exactly are you stuck?

Okay thanks ill take another look at the first problem and for the second problem the equation confuses me. What does the x*i mean?

is just a shorthand to give a label to each value of x.

Okay I get problem 2 all the way up to this point



What is the n^3/3 + ...