In the diagram below, the region between the graphs of y=2 sin¬x and y=rx, in the first quadrant, is shaded. Using integration with respect to the y-variable, calculate the area of the shaded region. Provide an exact answer using n as needed, and show and explain your work.

Q: SET UP the definite integral that will give the area of the shaded region using a. x as variable of…

A: According to question, we have to find area bounded by the curve, y2 = x+2,andy = x

Q: Find the area of the region that is enclosed between the curves a = y and x= y - 2 integrating with…

A:

Q: Use integration by parts to evaluate the integral. f2x si sin(x) dx + C

A:

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Evaluate the integral. (Use C for the constant of integration.) 6 arctan(Vx) dx

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

A:

Q: Sketch the region that lies between the curves y = 4 sin(x) and y = 3 cos(x) from x = 0 to x = 0.37.…

A:

Q: Use integration by parts to evaluate the indefinite integral. 3 arctan(5y) dy Answer = + C

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. dy…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 5+ 10 cos 0. [Hint: r < 0…

A:

Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum, and…

A:

Q: For evaluating the integral x tan-lr dx, we apply integration by parts technique with the…

A:

Q: Approximate the value of the given integral by completing parts (a) and (b) below. (a) Use the…

A:

Q: . Split the region between the two curves into two smaller regions, then determine the area by…

A:

Q: 2. Given the integral dy dx, Sketch the region of integration, reverse the order of integration and…

A:

Q: 3. Use the Trapezoidal and Simpson rule to approximate the value of x*dx, n= 6(use 4 decimal…

A: Given: ∫12x2 dx  We have to calculate the given interval by using Trapezoidal and Simpson rule with…

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. 5…

A:

Q: Given the integral dx Use the integral table to help you find the Anti Derivativ

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

A:

Q: Ex3: sketch the region of integration and write the equivalent integral with reversed order of the…

A:

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: The given integral is, I=∫t3e-t2dt Take the value as u=t2dudt=2tdt=12tdu

Q: Find the area between y = 5 and y = (x – 1) +1 with x > 0. If needed, round your limits of…

A:

Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In x lying…

A: Solution We have to find the Surface area generated by revolving about the y-axis the part of curve…

Q: Sketch the region of integration described by 2x cos(x) dy dx, write an equivalent integral (or…

A: When we integrate a function with two variables over a rectangular region, the conception of double…

Q: Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer. 3…

A:

Q: Sketch the region bounded above by the curve (9e^−x)*sin(πx), the x-axis, and x = 1, and find the…

A: We have to sketch the region bounded by the curve 9e-xsinπx, x-axis, and x=1, and also find the area…

Q: Evaluate the area of the shaded region shown below using dxd order of Integration. yA y = 1+x? 2 -X=…

A: Area of the shaded region is given as, Total Area=A1+A2+A3+A4 where Ai, i=1,2,3,4 is the area of…

Q: Split the region between the two curves into two smaller regions, then determine the area (in…

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. 1…

A:

Q: b) Sketch the region of integration and write an equivalent integral with the order of integration…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx Vx + xVx

A:

Q: Find the area between y = 1.5x + 4 and y = decimal places. – 3. Round your limits of integration and…

A: the given curves are: y=1.5x+4y=x2-3 we have to find the area between the given curves. we have to…

Q: Sketch the region whose area is represented by the definite integral. ▪4 5 dx y y 6F

A:

Q: SET UP the definite integral that will give the area of the shaded region using a. r as variable of…

A: (a). We have to calculate the area of shaded region using integration taking x as a variable of…

Q: Approximate the integral to three decimal places using the indicated rule. 9 cos(x) r0.9 dx;…

A:

Q: Find the area between y = 2x +2 and y x - 1. Round your limits of integration and answer to 2…

A: Solve for the area

Q: First make a substitution and then use integration by parts to evaluate the integral. dx

A:

Q: xcos(4x)dx

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 13 + 26 cos 0. [Hint: r ≤…

A:

Q: Split the region between the two curves into two smaller regions, then determine the area (in units)…

A:

Q: D. Set-up the definite integral that will give the area of the surface generated by revolving the…

A: D) Given arc is y=2x⋯⋯(1)   Arc revolving from x=0 to x=2. a) To find: area of the surface revolving…

Q: The value of (4xy- (sinx)³)dx + (x² + y9)dy (Correct to ONE decimal place) where C is the region…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. To evaluate the given…

Q: Sketch the region whose area is represented by the definite integral. dx 2 4 Use a geometric formula…

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. -3…

A:

Q: Using integration by parts, the integral f In(16x*) dx is equal to:

A:

Q: Sketch the region of integration and change the order of integration of the following integral: e dx…

A:

Q: SET UP the definite integral that will give the area of the shaded region using a. x as variable of…

A: Given query is to setup integral for area inclosed by given curves.

Q: Evaluate the integral. (Use C for the constant of integration.) 9e 9x dx

A:

Q: SET UP the definite integral that will give the area of the shaded region using a. x as variable of…

A:

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.