Quiz about Ch 5 Integration

Question 1

Given $$\int_1^4f\left(x\right)dx=5,$$ what is $$\int_1^4\left(2f\left(x\right)-1\right)dx$$ equal to?

Accepted Answer

$$7$$

Answer

$$4$$

Answer

$$10$$

Answer

$$0$$

Answer

$$9$$

Question 2

What is the value of the definite integral $$\int_1^3\left(3x^2+\frac{2a}{x^2}\right)dx,$$ where $$a$$ is a constant?

Accepted Answer

$$26+\frac{4a}{3}$$

Answer

$$26-\frac{8a}{3}$$

Answer

$$26-\frac{56a}{27}$$

Answer

$$28-\frac{8a}{3}$$

Question 3

Which one of the following statements is not true?

Accepted Answer

$$\int_{-1}^32dx=4$$

Answer

$$\int_{-2}^2x^3dx=0$$

Answer

$$\int_{-2}^2x^2dx=2\int_0^2x^2dx$$

Answer

$$\int_0^32xdx=\int_2^32xdx+\int_0^22xdx$$

Question 4

What is the indefinite integral $$\int_{ }^{ }\left(3x-2\right)^5dx$$ equal to?

Accepted Answer

$$\frac{\left(3x-2\right)^6}{18}+C$$

Answer

$$\left(3x-2\right)^6+C$$

Answer

$$\frac{\left(3x-2\right)^6}{6}+C$$

Answer

$$15\left(3x-2\right)^4+C$$

Question 5

Given $$\int_{-1}^2\left(kx+2\right)dx=4,$$ what is the value of $$k?$$

Accepted Answer

$$-\frac{4}{3}$$

Answer

$$-\frac{4}{5}$$

Answer

$$\frac{8}{3}$$

Answer

$$-\frac{2}{3}$$

Answer

$$\frac{2}{3}$$

Question 6

The graph of $$y=f\left(x\right)$$ passes through the point $$\left(2,-3\right),$$ and $$f$$

What is the equation of $$f\left(x\right)?$$

Accepted Answer

$$f\left(x\right)=x^3-x^2+x-9$$

Answer

$$f\left(x\right)=6x-2$$

Answer

$$f\left(x\right)=x^3-x^2+x+3$$

Answer

$$f\left(x\right)=x^3-x^2-8$$

Question 7

What is the area of the region enclosed by the curve $$y=x^3$$ and the x-axis, between $$x=-2$$ and $$x=3?$$

Accepted Answer

$$24\frac{1}{4}$$ units²

Answer

$$16\frac{1}{4}$$ units²

Answer

$$65$$ units²

Answer

$$16$$ units²

Answer

$$15$$ units²

Question 8

The line $$y=x+6$$ intersects the parabola $$y=x^2$$ at the points $$\left(-2,4\right)$$ and $$\left(3,9\right).$$

What is the area of the region contained between the line and the parabola?

Accepted Answer

$$20\frac{5}{6}$$ units²

Answer

$$18\frac{5}{6}$$ units²

Answer

$$8\frac{1}{6}$$ units²

Answer

$$26\frac{5}{6}$$ units²

Question 9

The graph of a function $$y=f\left(x\right)$$ is shown in the diagram. The graph consists of horizontal interval $$AB,$$ a quarter circle $$BC,$$ and an interval $$CD.$$

What is the value of the definite integral $$\int_0^6f\left(x\right)dx?$$

Accepted Answer

$$2+\pi$$

Answer

$$6+\pi$$

Answer

$$\pi-2$$

Answer

$$\pi$$

Question 10

By first differentiating $$\cos x^3,$$ what is the primitive of $$6x^2\sin x^3?$$

Accepted Answer

$$-2\cos x^3$$

Answer

$$\sin x^3$$

Answer

$$2\sin x^3$$

Answer

$$-\cos x^3$$

Question 11

Question 11.

Accepted Answer

11

Answer

5

Answer

9

Answer

15

Question 12

What is the value of $$\int_{-3}^2\left|x+1\right|dx\ ?$$

Accepted Answer

$$\frac{13}{2}$$

Answer

$$\frac{5}{2}$$

Answer

$$\frac{11}{2}$$

Answer

$$\frac{17}{2}$$

Question 13

Using the trapezoidal rule with 4 subintervals, which expression gives the approximate area under the curve $$y=xe^x\ $$ between $$x=1$$ and $$x=3\ ?$$

Accepted Answer

$$\frac{1}{4}\left(e^1+3e^{1.5}+4e^2+5e^{2.5}+3e^3\right)$$

Answer

$$\frac{1}{4}\left(e^1+6e^{1.5}+4e^2+10e^{2.5}+3e^3\right)$$

Answer

$$\frac{1}{2}\left(e^1+6e^{1.5}+4e^2+10e^{2.5}+3e^3\right)$$

Answer

$$\frac{1}{2}\left(e^1+3e^{1.5}+4e^2+5e^{2.5}+3e^3\right)$$

Question 14

The diagram shows the parabola $$y=4x-x^2$$ meeting the line $$y=2x$$ at $$\left(0,0\right)$$ and $$\left(2,\ 4\right).$$

Which expression gives the area of the shaded region bounded by the parabola and the line?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 15

The graph of $$y=f\left(x\right)$$ has been drawn to scale for $$\left[0,\ 8\right]$$ .

Which of the following integrals has the greatest value?

Accepted Answer

$$\int_0^2f\left(x\right)dx$$

Answer

$$\int_0^7f\left(x\right)dx$$

Answer

$$\int_0^8f\left(x\right)dx$$

Answer

$$\int_0^1f\left(x\right)dx$$

Answer

$$\int_2^6f\left(x\right)dx$$

Ch 5 Integration

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