Chapter 7.2, Problem 77E

Which of the following is the correct integral setup to find the area enclosed by the curves f(x) = 2-2x and g(x) =x^2 -1

How did du become 6x^2dx? So basically what I am asking is, where did the 6 derive from?

sinx Evaluate the integral dx 1-cOsx using Karl Weierstrass substitution.

2*) Showing all work, perform the given integral: | Vtan a(sec“ r)dr 3) Showing all work, and using integration by parts, perform the integral: | cos (In(x))dr Hint: This is a composition of functions, not a product. Use two tricks and watch your signs carefully

How can substitutions in single definite integrals be viewed as transformations of regions? What is the Jacobian in such a case? Illustrate with an example.

Evaluate the integral sec(theta)/sec(theta)-tan(theta) d(theta) A. sec2(theta) - tan(theta) + CB. tan(theta) + sec(theta) + CC. tan2(theta) + sec(theta) + C D. tan (theta) - sec(theta) +C please let me know if you need a picture. I wish i was able to format the integral better here.  sec(x)/sec(x)-tan(x) dx (this is to help if you don't understand the theta input)

Evaluate the definite integral. 6x dx Need Help? Read It Wa -/1 Points] DETAILS НА! Evaluate the definite integral. *4 (10 – 4x) dx Need Help? Read It -/1 Points] DETAILS НА Evaluate the definite integral. *3 (x² + 3)3x dx