Quiz about INTRODUCTION TO INTEGRATION

Question 1

Which method is suitable to find $$\int_{ }^{ }\left(\frac{5}{\sqrt[]{2x+7}}\right)dx$$ ?

Accepted Answer

Reverse chain rule

Answer

Reverse differentiation

Answer

Integration by parts

Answer

Use partial fractions

Question 2

Find $$\int_{ }^{ }\left(11x^{10}+10x^9\right)dx$$

Accepted Answer

$$x^{11}+x^{10}+c$$

Answer

$$11x^{11}+10x^{10}+c$$

Answer

$$x^{11}+10x^{10}+c$$

Answer

$$110x^{10}+90x^8+c$$

Question 3

Find $$\int_{ }^{ }\left(2+x^3+\frac{5}{x^3}\right)dx$$ .

Accepted Answer

$$2x+\frac{1}{4}x^4-\frac{5}{2x^2}+c$$

Answer

$$3x^2-20x^{-4}+c$$

Answer

$$2x-\frac{1}{4}x^4-\frac{5}{2}x^2+c$$

Answer

$$2+\frac{1}{4}x^4-\frac{5}{2}x^{-2}+c$$

Question 4

Without using integrate function at your calculator evaluate $$\int_{-5}^4\left(x^3+3x\right)dx$$

Accepted Answer

$$-105\ \frac{3}{4}$$

Answer

$$-105\ \frac{2}{3}$$

Answer

$$105\ \frac{1}{2}$$

Answer

$$105\ \frac{3}{2}$$

Question 5

Without using function integrate at your calculator evaluate $$\int_{0.5}^2\left(\frac{x^2+3x+4}{x^4}\right)dx$$

Accepted Answer

$$17.6$$

Answer

$$17.5$$

Answer

$$16.4$$

Answer

$$15.5$$

Question 6

Is it true the area of the shaded region is $$7.5\ unit^2$$ ?

Accepted Answer

No

Answer

Yes

Question 7

Find the area of the shaded region.

Accepted Answer

5.33

Answer

15.33

Answer

3.33

Answer

6.33

Question 8

A curve passes through the point $$\left(4,1 ight)$$ and its gradient at any point is given by $$\frac{ ext{d}y}{ ext{d}x}=2x-6$$ . Find the equation of the curve.

Accepted Answer

$$y=x^2-6x+9$$

Answer

$$y=x^2-6x+7$$

Answer

$$y=2x^2-6x+9$$

Answer

$$y=x^2-6x$$

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