arcsin x dx.

Q: Sketch the area that the definite integral represents and calculate the area geometrically (not…

A: Given, ∫x=1x=3x+2dx Now to sketch and evaluate the area of the above definite integral,

Q: Use a double integral to find the area of the shaded region.

A: The formula for the area of a region of a polar curve, r(θ) bounded by θ=a to θ=b in the polar…

Q: Sketch the area that the definite integral represents and calculate the area geometrically (not…

A: (A) We have the given definite integral which represent the area under the curve as A=∫13x+2dx On…

Q: Sketch the region bounded by the curves and find the area of that region.

A:

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

A: Given integration is, ∫sin-1lnxxdx Let, lnx=t⇒1xdx=dt

Q: Use double integrals to find the area inside the curve r = 5sin(e)

A: The given curve is:

Q: What is the area of the region bounded by the graph of r = 4 sin 2θ

A: What is the area of the region bounded by the graph of r = 4 sin 2θ

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

A:

Q: Consider the region bounded by the parabola y=4-x^2 and the x-axis. Set up a definite integral to…

A: Consider the following equation of curves: y=4-x2y=0 Points of intersection: 4-x2=0x2=4x=2,-2…

Q: Evaluate the integral by reversing the order of integration. Sketch the region.

A:

Q: Find the length of the curve y = arcsin e* fromx = 0 to x = In?. Show complete solution of points of…

A:

Q: 4. Sketch the region enclosed by y = 2x – x? and y = 0. Use calculus to find the exact area of this…

A: The solution is given below:

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: The given integral: ∫-π/4π/4tan x dx To sketch the area bounded by the given integral: Draw the…

Q: Sketch the region whose area is given by the definite integral. 8. x dx

A:

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: The given integral is,

Q: Find the area bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

Q: Find the area enclosed by the given curves (using applications of definite integrals).

A:

Q: Find the area of the region that bounded by r=1- cos(0)

A:

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

Q: dx 1 +sinx+cosx

A: LetI=∫dx1+sinx+cosxwe know…

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A:

Q: Use the Table of Integrals on the Reference Pages toevaluate the integral.

A: Evaluate: ∫4x2-4x-3dx

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. y = cosx,…

A:

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: Therefore, the value of the integral is 0.23286.

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: Solution:Given  Let         I=∫-11tan-1xdxTo sketch th signed area represented by the integral and…

Q: The diagram below shows an area enclosed between a parabola and a straight line. Determine this area…

A:

Q: Calculate the area of the region bounded by the graph of f(0) = cose sine and the 0 - axis between 0…

A: Consider the given function: fθ=cosθsinθ Area of a function fx in interval a,b is given by:…

Q: Give an example showing how to use rectangles to estimate the area under a curve.  Then use…

A: Let us choose a function f(x) = x2 and say that we want to calculate the ara under f(x) and x-axis…

Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: Find the area of the region. y = sin 8x

A:

Q: Sketch the region enclosed by the given curves and calculate its area. y=4-x to the power of 2, y=0

A: The given equation is

Q: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

A:

Q: Use a graph to give a rough estimate of the area of the region that lies beneath the given curve.…

A:

Q: etch the region enclosed by the curves and find its area

A: Here we have to sketch the region enclosed by the curve y=|x-2| and x-5y+10=0.  The required region…

Q: Find the area of the region that lies inside the first curve and outside the second curve. 3 - 3…

A: Let's find.

Q: Sketch the region bounded above by the curve 7e- sin(Tx), the x-axis, and x = 1, and find the area…

A: Given,

Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: Find the area bounded by y = 0.5(x- 2)² – 1 and the X-axis from x-3 to x-5. Show the sketch with…

A: y= 0.5(x-2)2-10 =0.5(x-2)2-11 = 0.5 (x-2)22 = (x-2)2x - 2 = ± 2x =2+2    x~ 3.414orx =2-2x ~ 0.586

Q: Find the area bounded by y = sin²(x) and y = sin³(x) from < i< .

A:

Q: Sketch the region whose area is given by the definite integral then use your sketch to find the area…

A: Sketch the graph of of the given definite integral.

Q: -1 sinx dx

A: Integration by parts:∫fgdx=f∫gdx-∫f'∫gdxdx

Q: Te* sin( –4x)dx

A: Find your answer below

Q: Find the area of the region bounded by the curves y = x andy = sin x from x = 0 to x = π.

A: We have to find the area of the region bounded by the curves y = x and y = sin x from x = 0 to x =…

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: To find the definite integral using geometry.

Q: Find the area of the region enclosed by one loop of the curve. r=sin(8theta)

A: Draw the given curve as shown below.

Q: Evaluate the integral -dx sinx-cosx

A:

Q: 3 dy dx 0 - 2x

A:

Q: Evaluate the integral using integration by parts. cos

A: We can solve as follows

Q: Find the area of the region between the curves y = sin(nx/2) and y = x. Area between curves =

A: In the question it is asked to calculate the area between two curves y=sin(πx2). and y=x.

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.