Facts Assessment #2

Question 1

∫ dx

Answer 1

x+C

Question 2

∫ x^n dx

Answer 2

x^n+1/n+1 +C

Question 3

∫ 1/x^n dx

Answer 3

x^-n+1/-n+1

Question 4

∫ 1/x dx

Answer 4

ln lxl +C

Question 5

∫ e^x dx

Answer 5

e^x +C

Question 6

∫a^x dx

Answer 6

a^x / lna +C

Question 7

∫ sinx dx

Answer 7

-cosx +C

Question 8

∫ cos x

Answer 8

sinx+c

Question 9

∫ sec^2 x dx

Answer 9

tan x +C

Question 10

∫ secx tanx

Answer 10

sec x +C

Question 11

∫ cscx cotx

Answer 11

-cscx +C

Question 12

∫ csc^2x dx

Answer 12

-cotx+c

Question 13

∫ 1/√1-x^2 dx

Answer 13

sin^-1x + C

Question 14

∫ -1/√1-x^2 dx

Answer 14

cos^-1x +C

Question 15

∫ 1/1+x^2 dx

Answer 15

tan^-1x +C

Question 16

What is added to the answer to each indefinite integral?

Answer 16

+C

Question 17

What is the geometric meaning of the definite integral?

Answer 17

Area between the function and x-axis

Question 18

When the bounds of the integral are reversed, how does the value of the integral change?

Answer 18

The answer is the negative of the original

Question 19

How is the area between the function and x-axis different when the area is below the x-axis?

Answer 19

When the area between the function and x-axis is under the x-axis, the area is negative.

Question 20

Riemann sums are used to approximate integrals by using what?

Answer 20

The areas of rectangles

Question 21

How do we use the left and right Riemann sums to calculate a trapezoidal approximation for a definite integral?

Answer 21

Take the average of the left and right Riemann sums

Question 22

When taking derivative of an integral, why do we multiply by the derivative of the bounds?

Answer 22

The chain rule

Question 23

When do we use u-substitution?

Answer 23

When the integral isn’t one of the integral formulas, we use u-substitution to transform the integral into one of the integration formulas.

Question 24

When using u-substitution, what happens to the integrals bounds?

Answer 24

Substitute the integrals bounds into the u=expression to get new bounds for the integral.

Question 25

How do we calculate the average value of f(x) on the interval (A, B)?

Answer 25

1/B-A ∫A B f(x)dx