Integral Calculus Exam Questions with Correct Grade A+ Solutions

Integral Calculus Exam Questions with Correct Grade A+ Solutions sin²x + cos² x=? - Correct Answers: 1 Which Pythagorean formula = 1? 1 + tan² x=? - Correct Answers: sec²(x) Which Pythagorean formula = sec²(x)? 1 + cot² x=? - Correct Answers: csc² x Which Pythagorean formula = csc² x sin(-x)=? - Correct Answers: -sin x -sin(x) = sin(-x) or only -sin(x)? d/dx (x^n) Rule? - Correct Answers: Power Rule Reverse the power rule for derivatives. d/dx (f*g) - Correct Answers: fg' + gf' Product Rule What is the product rule in reverse? d/dx (f/g) Rule? - Correct Answers: Quotient Rule When do you use the quotient rule? d/dx f(g(x)) Rule? - Correct Answers: Chain Rule When do you use the chain rule? d/dx (sin x)? - Correct Answers: cos x is the derivative of what? d/dx (cos x)? - Correct Answers: - sin x is the derivative of what? d/dx (tan x)? - Correct Answers: sec² x is the derivative of what? d/dx (cot x)? - Correct Answers: - csc² x is the derivative of what? d/dx (sec x)? - Correct Answers: sec x tan x is the derivative of what? d/dx (csc x)? - Correct Answers: -csc x cot x is the derivative of what? d/dx (e^x)? - Correct Answers: is the derivative of what? d/dx (a^x)? - Correct Answers: is the derivative of what? d/dx (ln x)? - Correct Answers: 1/x is the derivative of what? d/dx arcsin (x) ? - Correct Answers: is the derivative of what? d/dx arctan (x) ? - Correct Answers: is the derivative of what? d/dx (arcsec x)? - Correct Answers: is the derivative of what? ∫ a dx? - Correct Answers: ax + c is the integral of what? ∫ 1/x dx? - Correct Answers: ln | x | + c is the integral of what? ∫ e^x dx? - Correct Answers: e^x + c is the integral of what? ∫ a^x dx? - Correct Answers: a^x/ ln a + c is the integral of what? ∫ ln x dx? - Correct Answers: x ln x - x + c is the integral of what? ∫ sin x dx? - Correct Answers: -cos x + c is the integral of what? ∫ cos x dx? - Correct Answers: sin x + c is the integral of what? ∫ tan x dx? - Correct Answers: -ln |cos x| + c is the integral of what? ∫ cot x dx? - Correct Answers: ln |sin x| + c is the integral of what? ∫ sec x dx? - Correct Answers: ln |sec x + tan x| + c is the integral of what? ∫ csc x dx? - Correct Answers: -ln |csc x + cot x| + c is the integral of what? ∫ sec² x dx? - Correct Answers: tan x + c is the integral of what? ∫ sec x tan x dx? - Correct Answers: sec x + c is the integral of what? ∫ csc² x dx? - Correct Answers: - cot x + c is the integral of what? ∫ csc x cot x dx? - Correct Answers: - csc x + c is the integral of what? ∫ tan² x dx? - Correct Answers: tan x - x + c is the integral of what? ∫ dx/(a² + x²)? - Correct Answers: 1/a arctan (x/a) + c is the integral of what? ∫ dx/(sqrt(a² - x²))? - Correct Answers: arcsin (x/a) + c is the integral of what? What is the area of a circle geometrically? - Correct Answers: π(a²) a=radius is the area of what? Formula for integrating using the disk method? - Correct Answers: is the formula for what? Formula for integrating using the washer method? - Correct Answers: is the formula for what? Formula for integrating about the line x=0 using the shells method? - Correct Answers: Is the formula for what? What is the formula for integrating about the line y=0 using the shell method? - Correct Answers: Is the formula for what? What is the formula for Hooke's Law? - Correct Answers: Hooke's Law: F=kd is force (f) equals the spring constant (k) times the distance (d). ∫ sinh(x) dx - Correct Answers: cosh(x) + C Is the integral for what? ∫ cosh(x) dx - Correct Answers: sinh(x) + C Is the integral for what? ∫ tanh(x) dx - Correct Answers: ln(cosh(x)) + C Is the integral for what? ∫ coth(x) dx - Correct Answers: ln |sinh(x)| + C Is the integral for what? ∫ sech(x) dx - Correct Answers: sin⁻¹ (tanh(x)) + C Is the integral for what? ∫ csch(x) dx - Correct Answers: ln |tanh(x/2)| + C Is the integral for what? Arc Length Formula? - Correct Answers: Is the integral for what? Surface Area Formula? - Correct Answers: Is the integral for what? Surface Area of a Sphere? - Correct Answers: where a is a constant Is the formula for what? The formula for arccosh(x)? - Correct Answers: Is the formula for what? The formula for arcsinh? (x)? - Correct Answers: is the formula for what? The formula for arctanh? - Correct Answers: is the formula for what? The formula for the arcsech? - Correct Answers: is the formula for what? The formula for the arccsch? - Correct Answers: is the formula for what? The formula for the arccoth? - Correct Answers: is the formula for what? d/dx arccos(x)? - Correct Answers: Is the derivative for what? d/dx arccot(x)? - Correct Answers: Is the derivative for what? d/dx arccsc(x)? - Correct Answers: Is the derivative for what? d/dx arcsec(x)? - Correct Answers: Is the derivative for what? d/dx arccsc(x)? - Correct Answers: Is the derivative for what? integral of 1/sqrt(a^2-x^2) dx - Correct Answers: arcsin of (x/a) + C Is the integral for what? Integral of 1/sqrt(a^2+x^2) dx - Correct Answers: arcsinh of (x/a) + C Is the integral for what? Integral of 1/a^2+x^2 dx - Correct Answers: 1/a arctan (x/a) + C Is the integral for what? Integral of 1/(a^2-x^2) dx - Correct Answers: 1/a arctanh (x/a) + C Is the integral for what? Integral of 1/sqrt(x^2-a^2) dx - Correct Answers: arccosh (x/a) + C Is the integral for what? sin(pi/3)=? - Correct Answers: sqrt of 3 divided by 2 is the arcsin of what? sin(pi/4)=? - Correct Answers: sqrt of 2 divided by 2 is the arcsin of what? sin(pi/6)=? - Correct Answers: 1/2 is the arcsin of what? sin(pi/2)=? - Correct Answers: 1 is the arcsin of what? sin(0)=? - Correct Answers: 0 is the arcsin of what? cos(0)=? - Correct Answers: 1 is the arccos of what? cos(pi/2)=? - Correct Answers: 0 is the arccos of what? cos(pi/3)=? - Correct Answers: 1/2 is the arccos of what? cos(pi/4)=? - Correct Answers: the sqrt of 2 divided by 2 is the arccos of what? cos(pi/6)=? - Correct Answers: the sqrt of 3 divided by 1/2 is the arccos of what? tan(0)=? - Correct Answers: 0 what is the arctan of 0? tan(pi/6)=? - Correct Answers: the sqrt of 3 divided by 3 what is the arctan of sqrt(3)/3? tan(pi/4)=? - Correct Answers: 1 What is the arctan of 1? tan(pi/2)=? - Correct Answers: undefined in the first quadrant where is the arctan undefined? tan(pi/3)=? - Correct Answers: sqrt(3) What is the arctan of the sqrt of (3)? What is the shorthand for x-bar and y-bar? (COM) - Correct Answers: What is the C.O.M. formula for M(mass)? (COM or centroid of a lamina) - Correct Answers: What is the formula for the Moment about Y? (COM or centroid of a lamina) - Correct Answers: What is the formula for the Moment about X? (COM or centroid of a lamina)? - Correct Answers: Formula for sinh(x)? - Correct Answers: Is the formula for what function? What is the formula for cosh(x)? - Correct Answers: Is the formula for what function? What is the formula for tanh(x)? - Correct Answers: Is the formula for what function? What is the formula for sech(x)? - Correct Answers: Is the formula for what function? What is the formula for csch(x)? - Correct Answers: Is the formula for what function? What is the formula for coth(x)? - Correct Answers: Is the formula for what function? What is the formula for a collection of masses along a straight line? - Correct Answers: Is the formula for what?