Integrals in Summation Notation

Which of the limits is equivalent to the following definite integral?

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 $\int_2^5\left(x^3+3\right)dx$  as limit of a sum is equivalent to

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{1}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3i}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$  

 $\int_0^{\pi}\cos xdx\$  as limit of a sum is equivalent to

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{i}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{i}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{\pi}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{\pi}{n}$  

 $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{5i}{n}\right)^2+\frac{5i}{n}+1\right]\frac{5}{n}$  in integral notation would be 

•  $\int_0^5\left(x^2+x+1\right)dx$  

•  $\int_5^6\left(x^2+x+1\right)dx$  

•  $\int_0^1\left(\left(5x\right)^2+5x+1\right)dx$  

•  $\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx$  

 $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[2+\sqrt{3+\frac{4i}{n}}\right]\frac{4}{n}$  in integral notation would be 

•  $\int_3^7\left(2+\sqrt{x}\right)dx$  

•  $\int_0^4\left(2+\sqrt{x}\right)dx$  

•  $\int_3^7\left(2x+\sqrt{x}\right)dx$  

•  $\int_3^7\left(2+\sqrt{3+x}\right)dx$  

Which of the definite integrals is equivalent to the following limit?

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Which of the limits is equivalent to the following definite integral?

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Which of the definite integrals is equivalent to the following limit?

Careful with this one...

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Find F'(x)

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• B

• C

• D

Find F'(x)

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• B

• C

• D