Free Printable u-sub and area between curves

1.

Find the limits of integration for the area of the region enclosed by the graphs x = 2y² and x - y = 1.

a)

-1/2 to 2

b)

-1/2 to 1 and 1 to 2

c)

-1/2 to 1

d)

1 to 2

2.

(a)

3.

Find the area of the region bounded by the parabolas y = 2x - x² and y = x².

a)

3

b)

1

c)

-3

d)

1/3

4.

What should be used for u in solving the integral below
∫ (tan⁴xsec²x)dx

a)

tanx

b)

tan⁴x

c)

no u needed

d)

tanxsecx

5.

Solve the following integral. Leave your solution in term of u.
$\int\sqrt{4x-3}\ dx$

a)

$\frac{1}{6}\left(\sqrt{u^3}\right)+c$

b)

$\frac{2}{3}u^{\frac{3}{2}}+c$

c)

$\frac{1}{4}u^{\frac{1}{2}}+c$

d)

$\frac{1}{4}u^{\frac{3}{2}}+c$

6.

Rewrite the function in terms of u.

a)

b)

c)

d)

7.

Evaluate the integral.

a)

$-\frac{5}{4}\cos\left(2x^2\right)\ +\ c$

b)

$\frac{5}{4}\cos\left(2x^2\right)\ +\ c$

c)

$-\frac{5}{4}\cos\left(2x^2\right)$

d)

can't be integrated

8.

What should du equal in this integral?

a)

tanx secx dx

b)

secx dx

c)

sec²x dx

d)

tanx dx

9.

Find the area of the region enclosed by the lines and curves.

y = 3x + 4 and y = x² + 4

a)

9

b)

93/2

c)

9/2

d)

18

10.

Evaluate the indefinite integral.
$\int\ \frac{1}{x\ln^2x}dx$

a)

$\ln x\ +\ c$

b)

$-\frac{1}{2\ln x}+c$

c)

$-\frac{1}{\ln x}+c$

d)

$2\ln x\ +\ c$

11.

Evaluate the integral.
$\int_0^1x^2e^{2x^3-1\ }dx$

a)

$\frac{1}{6}\left(e\ -\ \frac{1}{e}\right)$

b)

$6\left(e\ -\ \frac{1}{e}\right)$

c)

$\frac{1}{6}\left(e\ -1\right)$

d)

$6\left(e-1\right)$

12.

(a)

u-sub and area between curves

Total questions: 12

Worksheet time: 46mins

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