Free Printable Integrals in Summation Notation

1.

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

a)

b)

c)

d)

2.

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

a)

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

b)

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

c)

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

d)

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

3.

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

a)

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

b)

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

c)

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

d)

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

4.

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

a)

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

b)

$\int_5^6\left(x^2+x+1\right)dx$

c)

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

d)

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

5.

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

a)

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

b)

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

c)

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

d)

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

6.

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

a)

b)

c)

d)

7.

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

a)

b)

c)

d)

8.

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

Careful with this one...

a)

b)

c)

d)

9.

Find F'(x)

a)

A

b)

B

c)

C

d)

D

10.

Find F'(x)

a)

A

b)

B

c)

C

d)

D

11.

Evaluate

(a)

12.

Evaluate

(a)

13.

Using the areas of each region given
$\int_a^df\left(x\right)=$

a)

6

b)

20

c)

2

d)

24

Integrals in Summation Notation

Total questions: 13

Worksheet time: 8mins

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