Given the graphs determine the integral to find the volume, if it is rotated about the x- axis (1, 1), y=x³ 0 Of(x)²-(x³)²]dx Of(x)²-(x³)²]dy OTS (2³)²-(r)²]dx O None of the Above

Q: ot) Evaluate the integral 9 L₁ (1x) — 4) da (|x|- dx - -7 using the net area of a region. Give the…

A: Here we have given an integral:

Q: b) (2 points) Find the exact value of the following integral. Show all your work. 1 5 + 2x + 3 4e" )…

A:

Q: (1 – x²)dx eTextbook and Media 2) V You answered correctly! Move on to the next part to add to…

A: According to guidelines we solve only first question.

Q: Let R be in the region in the first quadrantenclosed be the graph f(x)=sqrt cos(x), the graph…

A: The double integral over the region R bounded by the curve y=g(x) and y=f(x)  in the interval [a, b]…

Q: x + 1 dx i x² + 2x 0, 15. 8.

A: We have to solve

Q: alculate the area under the curve f (x) = 3x² from x-6 to x=10 without using the fundamental theorem…

A:

Q: use integration by parts to establish the reductionformula.

A: Integration by part formula: ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: 2 dx x3 - x

A: We will find the integral as following.

Q: Consider two functions y₁ = : f(x) and y2 = g(x), and that y₁ ‡ y2 except where they intersect. If…

A: Consider two functions  and , and that  except where they intersect.If these two functions intersect…

Q: What is the volume of the solid formed in part III?

A:

Q: he curves shown in the schematic are defined by the functions = 8 - x² and y = x². is desired find…

A: The given schematic expression is A-∬RdA-∫-22∫x28-x2dydx We have to find the area of the region.

Q: f(x) = 3/x on the intend 0<x<4

A:

Q: (2,4) (2, 2) (--2,0) Given a region R enclosed by the curves: (x-2)² y = 1 + sin( ¹ (77²) ₁ y = 4-₁…

A: This problem is an application of definite integral and let us set up the definite integrals for…

Q: QUESTION 9 (8 points) Use a change of variables to evaluate the following definite integral. S 6x dx…

A: The given integral is:∫12​(3x2+4)36x​ dx a.) Let u be the expression inside the parentheses in the…

Q: If g(x) > (x) on the interval [a,b), then the area between the curves for as xs bis given by: O A.…

A: See step 2.

Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: 5. Estimate the area under the graph of f(x) = 1 + 2x² from z = 1 to z = 3 using n = 4 rectangles…

A: a) The left endpoint approximation use the left end point of a sub interval…

Q: Find the integr dx 1-5 2Vx+2x

A:

Q: (а) 4.x dx -2 (b) / (2.² Зх + 6) dx

A:

Q: a) A function is given by f(x) = 5x³ -6x² +x -e*. Find the slope of the tangent line to this curve…

A: