Free Printable The Definite Integral

1.

The lower estimate is:

(a)

2.

The upper estimate is:

(a)

3.

Estimate using a trapezoidal sum

(a)

4.

a)

$\int_1^5\frac{e^x}{1+x}dx$

b)

$\int_{ }^{ }\frac{e^x}{1+x}dx$

c)

$\int_1^5\left(\frac{e^x}{1+x}\right)\left(x\right)$

d)

5.

a)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(2+\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

b)

$\sum_{i=1}^n\left(2+\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

c)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

d)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(i\right)^6\left(\Delta x\right)$

6.

a)

3

b)

-3

c)

-6

d)

0

7.

(a)

8.

a)

$2\pi$

b)

$4\pi$

c)

$-2\pi$

d)

4

9.

a)

$\frac{9}{2}-2\pi$

b)

$9-4\pi$

c)

$4.5+2\pi$

d)

13

e)

10.

(a)

11.

a)

$2\pi$

b)

4

c)

$\frac{1}{\arcsin\left(4x\right)}$

d)

0

12.

a)

b)

$\frac{9\pi}{4}-3$ and 1 respectively

c)

$2.25\pi+3$ and 4 respectively

d)

$1+4.5\pi$ and 4 respectively

13.

(a)

14.

a)

$\frac{38}{3}t$

b)

$\frac{3}{38}$

c)

$-\frac{3t}{38}$

d)

$-\frac{38}{3}$

e)

40, I mean 4t

15.

a)

$\int_7^{10}f\left(r\right)dr$

b)

$\int_7^2f\left(x\right)dx$

c)

$\int_{10}^7f\left(x\right)dr$

d)

0

16.

(a)

17.

a)

b)

c)

d)

$\frac{41}{6}$

e)

-1.5

The Definite Integral

Total questions: 17

Worksheet time: 12mins

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