AB Calculus Chapter 5 Review
I. KEY CONCEPTS:
 Finding Area = Integrate
 Using geometry to find area
b
1
 Average Value =
f ( x)dx
b  a a
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Using Fundamental Theorem to evaluate a definite integral
Finding the derivative of an integral function using 2nd part of Fundamental Theorem
Basic antiderivatives
o Polynomials, cosine, sine, tangent, cosecant, secant, cotangent, inverse sine, inverse cosine,
inverse tangent, inverse cotangent, inverse secant, inverse cosecant, ex, 1/x
Approximating area/integrals
o LRAM, RRAM, MRAM
o Trapezoidal Rule
o Simpson’s Rule
FnInt in your calculator
Properties of Integrals
o Additivity
o Swapping Bounds
o Zero Area
o Constant Multiple
Mean Value Theorem for Integrals
II. BOOK REVIEW PROBLEMS
 Pgs. 315–319
o #1–7, 11, 17, 18, 20, 24, 26, 27, 32, 34, 36, 38, 42, 51, 56
III. EXTRA REVIEW PROBLEMS
 A region is bounded by the x-axis and the function g(x) = x2 on the interval [0, 5].
o Estimate the area using a right Riemann sum with n = 5 rectangles of equal width.
o Estimate the area using a left Riemann sum with n = 5 rectangles of equal width.
o Estimate the area using a midpoint Riemann sum with n = 5 rectangles of equal width.
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Apprximate the area of the region bounded by f(x) = 3x2 + 1 and the x-axis on the interval [0, 6] using
three trapezoids of equal width.
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Estimate the area of the region bounded by h(x) = sin x and the x-axis on the interval [0, π] using the
trapezoidal rule with n = 4 trapezoids.
3x4
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If y 

t 3  3dt , find y’
x2
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Use a Simpson’s Rule with n = 4 subintervals to estimate the area between the x-axis and the function
h(x) = sin x on the interval [0, π].
5x
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Differentiate
 9b db .
2
x 2
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Calculate the exact area of the region bounded by j(x) = x3 + x and the x-axis on the interval [–1, 0].