Find the area of the shaded region. 22) y = (x 3)2 (2,1) (4,1) 4. C)- D) Evaluate the integral. 31/4 23) 3 sec 0 tan 0 do B) 32 C) -6~/2 D) -3/2 A) 0 in/3 4/3 X N/3

Q: A5. The value of the definite integral dx is b) - 8 c) 24 d) 1.5

A: We have to find the value of the given definite integral.

Q: 29) Find the area bounded by the curves y= In x, y = 2 In x and line x-e in the first quadrant.

A: I have given the answer in the next step. Hope you understand that

Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

A:

Q: Find the area outside the curver=3+2cose and inside the curve =3-3cose. A B C D M 4 A 2 5A 4 NY 2…

A:

Q: (Sy?-8X46) dx =?

A: We need to evaluate ∫045x2-8x+6dx

Q: Find the Area bounded by the curves y? = x and x = 2y – y².

A: Draw the graphs of the given curves and mark the intersection area.

Q: 2x4 1+x² a) [: dx b) [ cos² cos² 2x dr

A:

Q: 1) a) Find and -1 b) Using a graph, explain why the first integral in (a) gives the area, whereas…

A:

Q: Find the area that it encloses

A: The given curve is r=2-sinθ. From figure, it is observes that 0≤θ≤2π. Obtain the area using formula…

Q: la) Find the area of resion between two functions.

A:

Q: Use area to evaluate the integral 7x • ! 0 dx = dx, b>0. ...

A: NOTE: Refresh your page if you can't see any equations. . the given function is  which is the…

Q: I. Integral Evaluation. (40 points) Evaluate the following five integrals. | (5z* - 8z + 6z) dr. 1.…

A:

Q: 5 3) S-²³2 235-1 dx a) Briefly explain why this integral is improper.

A: Follow the procedure given below.

Q: Find each integral by substitution J6x(3x +1)'dx

A:

Q: -dz Q5/ (A) Find the value of the integral 3 where C is the circle z+2 = z(z+1)"*1

A:

Q: 11) Find each integral by substitution a) Jóx(3x' +1)'dx 10x+1 b) ] (5x +x+8)

A: (a)∫6x3x2+18dx Let 3x2+1=u The derivative of the above equation. 6x+0=dudx6xdx=du Substitute the…

Q: Use U-substitution to find the integral: 2 1 dx

A: Given,          ∫1x22-1xdx

Q: 18. Sx²Vx3 – 4 dx a) Let u =x^3-4 b) Find du c) Find dx d) Evaluate the integral…

A: a) Let u=x3-4So, du=3x2dxor, dx=du3x2

Q: c/sechudu= tan -' Csinho) +c C.

A: To prove:- ∫ sechu du =tan-1(sinhu) +C

Q: point (e) by Using secant method

A: NOTE: According to guideline answer of first question can be given, for other please ask in 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.