1)Express the given integral as the limit of a Riemann sum but do not evaluate: Attached

2) Use the Fundamental Theorem to evaluate the integral : Attached

Question

1)Express the given integral as the limit of a Riemann sum but do not evaluate: Attached

2) Use the Fundamental Theorem to evaluate the integral : Attached

tmagloire1 · Answer

Here is the integral for both questions : http://prntscr.com/9y8a1u

freckles · Answer

$$\int\limits_a^b f(x) dx=\lim_{n \rightarrow \infty} \sum_{i=1}^{n} f(a+i \Delta x) \cdot \Delta x \ \text{ where } \Delta x =\frac{b-a}{n}$$

freckles · Answer

it should be easy to identify a and b and just plug them into the right hand side of the equation

freckles · Answer

and then identify f and plug in a+i(b-a)/n into that

freckles · Answer

you power rule for antiderivatives for number 4:
$$\int\limits x^{n} dx=\frac{x^{n+1}}{n+1}+C$$

freckles · Answer

where n can be anything but -1

tmagloire1 · Answer

Thank you @freckles! For the second question, am I supposed to use the power rule and then find the anti derivative?

freckles · Answer

yes