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

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

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

Evaluate the sums in 25. 5Σk=1 k(3k + 5) 26. 7Σk=1 k(2k + 1)

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

Lifting a Rope and Integration

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

Evaluate the sums in 27. 5Σk=1 k^3/225 + (5Σk=1 k)^328. (7Σk=1 k)^2 - 7Σk=1k^3/4

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

Evaluate the integral.π/42 sec2(t) dt0

Calculus Help: Integral ∫ sech^2 ⁡x dx, ∫ csch^2⁡ x dx - Hyperbolic Functions

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

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

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

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 53. y = 2x

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

Find the limits some other way.71. limx➡️inf (2^x-3^x)/(3^x+4^x)72. lim x➡️-inf (2^x+4^x)/(5^x-2^x)

53.Wilson lot size formula One of the formulas for inventory management says that the average weekly