Finding Indefinite Integrals In Exercises 49-52, find the most general antiderivative or indefinite

Finding Indefinite Integrals In Exercises 45-48 , find the most general antiderivative or indefinite

Learn to evaluate using the definite integral with square root

evaluate the integrals in 41. 1∫3 7 dx 42. 2∫0 5x dx

graph the function and find its average value over the given interval.58. ƒ(x) = 3x^2 - 3 on [0, 1]

65. xy + 2x + 3y = 1;66. x^2 + xy + y^2 - 5x = 2;67. x^3 +4xy-3y^(4/3) =2x;68.5x^(4/5)+10y^(6/5)=15

Finding Indefinite Integrals In Exercises 65–70, find the most general antiderivative or indefinite

Checking Antiderivative Formulas Verify the formulas in Exercises 71–74 by differentiation

Calculus - Integral (2x+1)/(x^2-5x+4) dx - Partial Fractions (Request)

81. If av(ƒ) really is a typical value of the integrable function ƒ(x) on [a, b] , then the constant

Finding Indefinite Integrals In Exercises 57-60, find the most general antiderivative or indefinite

Finding Indefinite Integrals In Exercises 25–70, find the most general antiderivative or indefinite

In Exercises 1–24, find an antiderivative for each function. Do as many as you can mentally.

find a formula for the Riemannsum obtained 46. ƒ(x) = x^2 - x^3 over the interval [-1, 0].

evaluate the integrals in 27. ƒ(x) = √(4 - x^2) on a. [-2, 2] , 28. ƒ(x)=3x + √(1- x^2) on a. [-1,0]

find the total area between the region and the x-axis.59. y = x^3 - 3x^2 + 2x, 0 ≤ x ≤ 2

13. Suppose that ƒ is integrable and that 3∫0 ƒ(z) dz = 3 and 4∫0 ƒ(z) dz = 7. Find a. 4∫3 ƒ(z) dz

use a definite integral to find the area of the region between the given curve and 52.y = πx^2

find a formula for the Riemann sum obtained 42. ƒ(x) = 3x^2 over the interval [0, 1].

use a definite integral to find the area of the region between the given curve and 53. y = 2x