(8) Find the area under the curve f(x) = e* – 1 from X =1 to x 2 Leave the answer with e, don't use the calculator to evaluate more.

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x – x² and the x-axis.

A:

Q: 1. Find the area between the curve f(x)=√x and g(x) = x³.

A:

Q: 18. Use limits to find the area between the graph of the function and the x axis given by the…

A: I have stated the used formula in the solution

Q: Estimate the area under the graph of x) - 5 cos(x) from xO to xR/2 using four approximating…

A:

Q: use a definite intergal to find the area under the curve between the give x-values. f(x)=2ex from…

A: Given data: f(x)=2ex from x=0 to x=ln4

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

Q: Find the area under the curve y = - over the interval [4, 9]. (4x + 2)² Enter the exact answer. area…

A:

Q: Calculate an approximate value of the integral ; dx by dividing the 1+x2 interval into 8 equal parts…

A:

Q: Find the most general antiderivative or indefinite integral. dx

A:

Q: 1 x2 1. Calculate an approximate value of the integral , dx by dividing the 1+x3 interval into 4…

A: Given function is, ∫01x21+x3

Q: # 8) Find the area under the curve. y 4-x

A:

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x - x and the x-axis. %3D

A:

Q: - e*) sinh x + e* cosh x + ex In the indefinite Integral in(cosh x + ex). A In(cosh x + e*)- sinh x…

A:

Q: Find the exact area under the curve between the indicated values of x. 3 ; between x = 1 and x = 3

A:

Q: (11) Find the area under the curve y =x+1 for 0<x<2 %3D

A:

Q: Find the exact area under the curve between the indicated values of x. y = -x2 + 9; between x = 0…

A:

Q: 4. Find the approximate area under the curve f(x) = x³ – 3x² + 7 on the interval [0.97,3.4]. Use…

A:

Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

A:

Q: 22 What is the area f(.x) under the line x) = 6 – x above the interval from x to 6? What is the…

A:

Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

A:

Q: Find the average value of the given function from x=0 to x=1. Sketch graph of the function, roughly…

A: Average value of a function y=f(x)  from x=a to x=b is given by Aavg=1b-a∫x=ax=bf(x)dxsee below the…

Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

A:

Q: 18. Use limits to find the area between the graph of the function and the x axis given by the…

A:

Q: The area between the curves y =2 cos (x) + 4 and y = 2 – 2 cos (x) on the interval [0, 1] is: 27 3 3…

A:

Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

A:

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral     e x  / (3…

A: We have to evaluate the integral: ∫ex3-e2xdx Rearranging the given integral, ∫ex3-ex2dx In this case…

Q: Find the area under y = 2 sin(x) + 2 cos(x) and above the x-axis from x = 0 to x = Tt/2. Leave your…

A: The given function is,

Q: Find the area under the curve f(x) =x+3x+7, above the X axis from x=4 to x=6.

A:

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

A:

Q: 1. Solve the area bounded by the curve (x - 2)² = - ( y - 4) and the lines x=- 2 and y= 4.

A: The area bounded by the curves (x-2)2=-(y-4) ,x=-2, y=4 is as shown above.

Q: The question is "What is the area under the curve at the right?" How and what are the steps to…

A:

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = 6e^x…

A:

Q: 1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point…

A:

Q: 1. Find the area under the curve of y on the interval [1, 4).

A:

Q: Find the exact area below the curve y = x°(1 – x) and above the x-ax is. %3D

A: y=x31-x Diagrammatic representation of the required area is,

Q: Find the areas between the curves y = 2(log2 x)/x and y = 2(log4 x)/x and the x-axis from x = 1 to x…

A: To determine the area between the curves and the x-axis.

Q: 1. Evaluate the integral using the Table of Integrals on Reference Pages 6 – 10. Sx'sin"(x*)&x (…

A:

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: 3. Use a definite integral to find the area under the curve y = 5 + 2x over the interval [-2,1] and…

A:

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x- x and the x-axis.

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 4. Find the area under the curve y = Vx +6 from x = -6 to x = 3. Give exact answer.

A:

Q: Find the area between the curve y = tan x and the x-axis from x = -π/4 to x = π/3

A: y=tanx from x=-π4 to x=π3. The graph is,

Q: Approximate the area under the curve y=f(x) between x=-1 and x=5 using Simpson's rule with n=6…

A:

Q: 3 Find the area under the curve y over the interval [3, 8] (4x + 2)?

A:

Q: 5. Find the area under the curve integrate 2/(9 - x ^ 2) dx

A: Given;           ∫29-x2 dx Take the constant out: ∫a.fx dx=a.∫fx dx           =2.∫19-x2 dx Apply…

Q: 1. Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y=−x^2+8x between x=3 and…

A:

Q: The area under the curve y =3/x over the interval [1.4]is equal to: 14

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.