INTEGRAL CALCULUS EXAM
QUESTIONS WITH COMPLETE
SOLUTIONS
d/dx arcsin (x) ? - ANSWER-is the derivative of what?
d/dx arctan (x) ? - ANSWER-is the derivative of what?
d/dx (arcsec x)? - ANSWER-is the derivative of what?
∫ a dx? - ANSWER-ax + c
is the integral of what?
∫ 1/x dx? - ANSWER-ln | x | + c
is the integral of what?
∫ e^x dx? - ANSWER-e^x + c
is the integral of what?
∫ a^x dx? - ANSWER-a^x/ ln a + c
is the integral of what?
∫ ln x dx? - ANSWER-x ln x - x + c
is the integral of what?
∫ sin x dx? - ANSWER--cos x + c
is the integral of what?
∫ cos x dx? - ANSWER-sin x + c
is the integral of what?
∫ tan x dx? - ANSWER--ln |cos x| + c
is the integral of what?
∫ cot x dx? - ANSWER-ln |sin x| + c
is the integral of what?
∫ sec x dx? - ANSWER-ln |sec x + tan x| + c
is the integral of what?
∫ csc x dx? - ANSWER--ln |csc x + cot x| + c
is the integral of what?
, ∫ sec² x dx? - ANSWER-tan x + c
is the integral of what?
∫ sec x tan x dx? - ANSWER-sec x + c
is the integral of what?
∫ csc² x dx? - ANSWER-- cot x + c
is the integral of what?
∫ csc x cot x dx? - ANSWER-- csc x + c
is the integral of what?
∫ tan² x dx? - ANSWER-tan x - x + c
is the integral of what?
∫ dx/(a² + x²)? - ANSWER-1/a arctan (x/a) + c
is the integral of what?
∫ dx/(sqrt(a² - x²))? - ANSWER-arcsin (x/a) + c
is the integral of what?
What is the area of a circle geometrically? - ANSWER-π(a²) a=radius
is the area of what?
Formula for integrating using the disk method? - ANSWER-is the formula for what?
Formula for integrating using the washer method? - ANSWER-is the formula for what?
Formula for integrating about the line x=0 using the shells method? - ANSWER-Is the
formula for what?
What is the formula for integrating about the line y=0 using the shell method? -
ANSWER-Is the formula for what?
What is the formula for Hooke's Law? - ANSWER-Hooke's Law: F=kd is force (f) equals
the spring constant (k) times the distance (d).
∫ sinh(x) dx - ANSWER-cosh(x) + C
Is the integral for what?
∫ cosh(x) dx - ANSWER-sinh(x) + C
Is the integral for what?
∫ tanh(x) dx - ANSWER-ln(cosh(x)) + C
Is the integral for what?
QUESTIONS WITH COMPLETE
SOLUTIONS
d/dx arcsin (x) ? - ANSWER-is the derivative of what?
d/dx arctan (x) ? - ANSWER-is the derivative of what?
d/dx (arcsec x)? - ANSWER-is the derivative of what?
∫ a dx? - ANSWER-ax + c
is the integral of what?
∫ 1/x dx? - ANSWER-ln | x | + c
is the integral of what?
∫ e^x dx? - ANSWER-e^x + c
is the integral of what?
∫ a^x dx? - ANSWER-a^x/ ln a + c
is the integral of what?
∫ ln x dx? - ANSWER-x ln x - x + c
is the integral of what?
∫ sin x dx? - ANSWER--cos x + c
is the integral of what?
∫ cos x dx? - ANSWER-sin x + c
is the integral of what?
∫ tan x dx? - ANSWER--ln |cos x| + c
is the integral of what?
∫ cot x dx? - ANSWER-ln |sin x| + c
is the integral of what?
∫ sec x dx? - ANSWER-ln |sec x + tan x| + c
is the integral of what?
∫ csc x dx? - ANSWER--ln |csc x + cot x| + c
is the integral of what?
, ∫ sec² x dx? - ANSWER-tan x + c
is the integral of what?
∫ sec x tan x dx? - ANSWER-sec x + c
is the integral of what?
∫ csc² x dx? - ANSWER-- cot x + c
is the integral of what?
∫ csc x cot x dx? - ANSWER-- csc x + c
is the integral of what?
∫ tan² x dx? - ANSWER-tan x - x + c
is the integral of what?
∫ dx/(a² + x²)? - ANSWER-1/a arctan (x/a) + c
is the integral of what?
∫ dx/(sqrt(a² - x²))? - ANSWER-arcsin (x/a) + c
is the integral of what?
What is the area of a circle geometrically? - ANSWER-π(a²) a=radius
is the area of what?
Formula for integrating using the disk method? - ANSWER-is the formula for what?
Formula for integrating using the washer method? - ANSWER-is the formula for what?
Formula for integrating about the line x=0 using the shells method? - ANSWER-Is the
formula for what?
What is the formula for integrating about the line y=0 using the shell method? -
ANSWER-Is the formula for what?
What is the formula for Hooke's Law? - ANSWER-Hooke's Law: F=kd is force (f) equals
the spring constant (k) times the distance (d).
∫ sinh(x) dx - ANSWER-cosh(x) + C
Is the integral for what?
∫ cosh(x) dx - ANSWER-sinh(x) + C
Is the integral for what?
∫ tanh(x) dx - ANSWER-ln(cosh(x)) + C
Is the integral for what?
