Integration II - Ambitious

Question 1: Find the antiderivative of the function

f (x) = {(2 x + 5)}^{2}

A

F (x) = \frac{x^{3}}{3} + 5 x^{2} + 25 x + C

B

F (x) = \frac{x^{3}}{3} + \frac{x^{2}}{2} + 25 + C

C

F (x) = \frac{4 x^{3}}{3} + 5 x^{2} + 25 x + C

D

F (x) = \frac{4 x^{3}}{3} + 5 x^{2} + 25 x

Question 2: Find the antiderivative of the function

f (x) = {(2^{6 x})}^{2}

A

F (x) = \frac{2^{12 x}}{12 \ln (2)}

B

F (x) = \frac{2^{12 x}}{\ln (2)} + C

C

F (x) = 2^{12 x} + C

D

F (x) = \frac{2^{12 x}}{12 \ln (2)} + C

Question 3: Find the antiderivative of the function

f (x) = \frac{1}{\cos^{2} (2 x)}

A

F (x) = \frac{1}{2} \tan (2 x) + C

B

F (x) = \frac{1}{2} \tan (x) + C

C

F (x) = \tan (2 x) + C

D

F (x) = \frac{1}{2} \tan (2 x)

Question 4: Find the equation of integral for the area of the shaded region:

A

S = \int (x^{2} - (x + 1)) d x

B

S = \int (x^{2}) d x

C

S = \int (x + 1) d x

D

S = \int ((x + 1) - x^{2}) d x

Question 5: Find the antiderivative of the function

f (x) = \frac{1}{21 + x^{2}}

A

F (x) = \frac{1}{\sqrt{21}} \arctan (x) + C

B

F (x) = \frac{1}{\sqrt{21}} \arctan (\frac{x}{\sqrt{21}}) + C

C

F (x) = \arctan (\frac{x}{\sqrt{21}}) + C

D

F (x) = \frac{1}{\sqrt{21}} \arctan (\frac{x}{\sqrt{21}})

Question 6: Calculate

\int_{π}^{2 π} (- \sin (\frac{x}{3})) d x

A

0

B

- \frac{1}{3}

C

- 3

D

1

Question 7: Calculate

\int_{0}^{3} ({(\frac{4}{9} x)}^{2} - 2) d x

A

\frac{38}{9}

B

5

C

- \frac{38}{9}

D

- \frac{38}{3}

Question 8: Calculate

\int_{0}^{1} (5^{x} + 1) d x

A

\frac{5}{\ln (5)} - 1

B

\ln (5)

C

\frac{4}{\ln (5)} - 1

D

- 1

Question 9: Calculate the area of the figure defined by

y = x^{2}

and

y = 1

A

\frac{3}{4}

B

2

C

1

D

\frac{4}{3}

Question 10: Calculate the area of the figure defined by

y = 2 x

,

x = 2

and

y = 0

A

4

B

2

C

5

D

- 4

Test: Integration II - Ambitious

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