Evaluate each integral using GEOMETRY. Draw a picture, and show your work. a. (2x-4)dx SV4-x'dx b.

Q: dx Evaluate the integral / by completing the square and using x² + 4x + 20 trigonometric…

A: integration with subsitution

Q: et dx 1+ea

A: Given, The integral ∫ex1+exdx We have to evaluate the integral.

Q: Consider S dx. Using trigonometric substitution, what is the integral fom in terms of 03

A: Given: ∫x2-9x3dx Using trigonometric substitution, we have to write the integral form in terms of θ.…

Q: Find the trigonometric integral.

A: Use the trigonometric identity as follows:

Q: Complete the table by identifying u and du for the integral. u = g(x) du = g'(x) dx du = dx u = xp 6…

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

Q: Calculate each integral, assuming all circles are positively oriented: dz, where y is the line…

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

Q: e Vx dx

A: We will put  (√x = t or u) then we will integrate it

Q: When the integral is evaluated by trigonometric substitution, e*V4 – e2x

A:

Q: Suggest a trigonometric substitution for each integral, and then write the new integral that results…

A:

Q: Evaluate the integral by completing the square and using trigonometric substitution.

A: ∫1x2+6x+62dx=∫1x+32-32dxSubstitute u = x+3=∫1u2-32du=∫1123u+3+112u+32-1123u-3+112u-32duApply the Sum…

Q: Evaluate the Integral (9ze" )dz + C

A: Evaluate the integral.      ∫9xex+5 dx

Q: Evaluate the integral using FTC I.

A: Solve the integral ∫(4x-9x2)dx by using the general power rule of the integration that is…

Q: Find the integrals using Trigonometric substitutions 1 (a) / Va? – x² dx (g) - 4.x2

A:

Q: Tπ L2 sin3xdx Tπ 4

A:

Q: 4. S cot?x csc x dx

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost other…

Q: Find the integral: J 3sinhæ-5cosha da Select one: a. -글arccos를 + C b. 글arcsec를 +C c. 글aresin를 +C…

A:

Q: Find the area inside the limacon = 7+ 6 sin 0. OA) 134T - 84 B) 67T + 84 OC) 67 T OD) 134T

A:

Q: 1 – 7w² dw

A:

Q: Complete the table by identifying u and du for the integral. u = g(x) du = g'(x) dx | (tan(x))5…

A:

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

A:

Q: Write the x and y coordinates of any point on the unit circle in terms of the angle theta…

A:

Q: c) Seax.Sinbx. dx =? Calculate the integral

A:

Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: dx Evaluate the integral/ by completing the square and using trigonometric substitution. V36x+6x2…

A: Given,  ∫dx36x+6x2  We have to evaluate the integral

Q: x2 — бх + 9 dx V6x – x2

A: We have to find value of given Integral

Q: Match each integral and its substituted form with the proper substitution. |(15x -10)3x²-4x+11 dx…

A:

Q: Sa cosxcos(sinx)dx

A:

Q: Evaluate the integral using FTC I.

A:

Q: dx 2. S XVx4+1

A:

Q: Evaluate the indicated integrals if b is a positive real number constant. A. ftan () dx B. dx C.…

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 29 VT dx = 17c +C

A:

Q: Find the integral by trigonometric substitution: * [V1- Tu /1– 7w² dw

A: Let I=∫1-7w2dw Putting w=17sinx dw=17cosxdx So,  I=17∫1-sin2xcosxdxI=17∫cos2xdx…

Q: evaluate the integral by completing the square and using trigonometric substitution.

A:

Q: Explain why each of the following integrals is improper  integral 0  to pie/4   cot x dx

A:

Q: c) S arc cot x dx

A:

Q: Using iterated integrals, find the smaller area cut form the circle x² + y2 = 16 and the line y =-1.

A: to find the area we consider th strip parallel to y axis  and desctribed the region as below

Q: dx Evaluate the integral / by completing the square and using trigonometric substitution x² + 4x +…

A: Solve the following integral

Q: Evaluate the integral.

A: To evaluate: ∫dxx2-4x Given integral can be re-written as: ∫dxx2-4x=∫1x2-4x+4-4dx=∫1x-22-22dx We…

Q: Sin X' cOS X dxN 9x2 16-x3 dx

A: 1. Given integral is ∫π4π3sinx·cosx dx Substituting  sinx=u ⇒cosx dx=du Hence, limits becomes,…

Q: Use the Rectangle Property to evaluate the following integral. -3 (-14) dx = %3D

A: given integral :

Q: Evaluate the integral and choose the correct answer. fxe² dx O Ọ xe ttc o xe etc Ọ - xẻ +C xe - 2e +…

A: Topic = Integration

Q: Utilize trigonometric substitution to evaluate the following integral: x*dx S- V8- 2x*

A:

Q: Complete the table by identifying u and du for the integral. u = g(x) du = g'(x) dx xp | (tan(x))"…

A: We know that the derivative of tan x is = sec2(x) = (sec(x))2

Q: Use the Rectangle Property to evaluate the following integral. -5 (-13) dx 10

A:

Q: Evaluate the integral using FTC I.

A:

Q: Complete the table by identifying u and du for the integral. u = g(x) du = g'(x) dx | (tan(x))?…

A:

Q: Evaluate the integral. 17xe dx +C %3D ENOTE: Enter the exact answer.

A:

Q: √ √ 1 √x² - 2x + 5 dx

A: Indefinite Integration

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integral (Trigonometric Substitution) |(a?x* – x®)&dx 6. x³)Zdx

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.