Question 1

Evaluate the following definite integral: $$\$$int_0$$^\pi \sin x \, dx.$$

Accepted Answer

$$2$$

Question 2

Which of the following is the correct value for $$\$$int_0$$^1 x^2$ \, dx$$?

Accepted Answer

$$\frac{1}{3}$$

Question 3

Given the region $$D in $$the $$xy-$$plane bounded by $$x=2$$, $$x=5$$, $$y=1$$, and $$y=4$$, what is the area of $$D$$?

Accepted Answer

$$12$$

Question 4

Evaluate $$\$$int_0$$^1 \sqrt{x} \, dx.$$

Accepted Answer

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

Question 5

Which of the following is the correct value for $$\$$int_0$$^\pi x \, dx$$?

Accepted Answer

$$\frac{\pi^2$}{2}$$

Question 6

If $$f(x) = x^3$, what is $$\$$int_1^2 f(x$$) \, dx$$?

Accepted Answer

$$\frac{15}{4}$$

Question 7

Find the value of $$\$$int_0$$^1 (2x + 3) \, dx.$$

Accepted Answer

$$4.5$$

Question 8

Which of the following is the correct value for $$\$$int_0$$^1 x^3$ \, dx$$?

Accepted Answer

$$\frac{1}{4}$$

Question 9

Evaluate $$\$$int_0$$^2 (x^2$ - x) \, dx.$$

Accepted Answer

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

Question 10

A rectangular region $$D in $$the $$xy-$$plane has vertices at $$(2,1)$$, $$(5,1)$$, $$(5,4)$$, and $$(2,4). $$What is the value of $$\iint_D 1 \, dA$$?

Accepted Answer

$$12$$

Question 11

Evaluate $$\$$int_0$$^\pi \cos x \, dx.$$

Accepted Answer

$$0$$

Question 12

Which of the following is the correct value for $$\$$int_0$$^1 (1 - x^2$) \, dx$$?

Accepted Answer

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

Question 13

Find the value of $$\$$int_0$$^2 x \, dx.$$

Accepted Answer

$$2$$

Question 14

Evaluate $$\$$int_0$$^1 (3x^2$ + 2x + 1) \, dx.$$

Accepted Answer

$$2.5$$

Question 15

Which of the following is the correct value for $$\$$int_0$$^1 x^4$ \, dx$$?

Accepted Answer

$$\frac{1}{5}$$

Question 16

Evaluate $$\$$int_0$$^2 (x^2$ + 2x + 1) \, dx.$$

Accepted Answer

$$8$$

Question 17

A region $$D in $$the $$xy-$$plane is bounded by $$x=0$$, $$x=3$$, $$y=0$$, and $$y=2. $$What is the value of $$\iint_D x \, dA$$?

Accepted Answer

$$6$$

Question 18

Evaluate $$\$$int_0$$^1 (2x^3$ - x^2$ + 4) \, dx.$$

Accepted Answer

$$4.25$$

Question 19

Which of the following is the correct value for $$\$$int_0$$^1 (x^2$ + x + 1) \, dx$$?

Accepted Answer

$$1.5$$

Question 20

Evaluate $$\$$int_0$$^2 (x^3$ - 2x^2$ + x) \, dx.$$

Accepted Answer

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

Study Notes: Double Integrals and Change of Variables in Multivariable Calculus

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