Facts Assessment #2 Flashcards
∫ dx
x+C
∫ x^n dx
x^n+1/n+1 +C
∫ 1/x^n dx
x^-n+1/-n+1
∫ 1/x dx
ln lxl +C
∫ e^x dx
e^x +C
∫a^x dx
a^x / lna +C
∫ sinx dx
-cosx +C
∫ cos x
sinx+c
∫ sec^2 x dx
tan x +C
∫ secx tanx
sec x +C
∫ cscx cotx
-cscx +C
∫ csc^2x dx
-cotx+c
∫ 1/√1-x^2 dx
sin^-1x + C
∫ -1/√1-x^2 dx
cos^-1x +C
∫ 1/1+x^2 dx
tan^-1x +C
What is added to the answer to each indefinite integral?
+C
What is the geometric meaning of the definite integral?
Area between the function and x-axis
When the bounds of the integral are reversed, how does the value of the integral change?
The answer is the negative of the original
How is the area between the function and x-axis different when the area is below the x-axis?
When the area between the function and x-axis is under the x-axis, the area is negative.
Riemann sums are used to approximate integrals by using what?
The areas of rectangles
How do we use the left and right Riemann sums to calculate a trapezoidal approximation for a definite integral?
Take the average of the left and right Riemann sums
When taking derivative of an integral, why do we multiply by the derivative of the bounds?
The chain rule
When do we use u-substitution?
When the integral isn’t one of the integral formulas, we use u-substitution to transform the integral into one of the integration formulas.
When using u-substitution, what happens to the integrals bounds?
Substitute the integrals bounds into the u=expression to get new bounds for the integral.
How do we calculate the average value of f(x) on the interval (A, B)?
1/B-A ∫A B f(x)dx
