Use the specifie substitution to find or evaluate the Integral. (Use C for the constant of Integration.) х — 3 dx, u = Vx - 3 x + 8

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) e40…

A: We have to find

Q: 3tan a sec? x dx (4+3tan=)* 2

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

A:

Q: Consider the following. 8x dx ex/2 Find a substitution to rewrite the integrand term ex as du. u =…

A: Here we consider the following we find a substitution rewrite the integrandterm e8x as…

Q: Reverse the order of integration and then evaluate. So S, x? sin(xy)dxdy а.

A: Let's find.

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) yV 6 +…

A:

Q: b. I = S(1+ sin x)5 cos x dx

A:

Q: Use the value of the first integral I to evaluate the two given integrals. 3 9 4 3 (8х-2x3) dx b. J…

A:

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

A:

Q: I = S(1+ sin x)³ cos x dx

A:

Q: Q2/ Evaluate the integral: 6. xe' dy dx by changing the order of integration.

A:

Q: Evaluate the integrals using the indicated substitutions.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: a*cosx dx,a is a constant s

A: Given: ∫axcosx dxa is constant

Q: Evaluate the integral. (Use C for the constant of integration.) 6.3 t0.5 0.5 6e*) dx 6.

A:

Q: (a) Change the order of integration and hence evaluate fo M*(ry)dydx.

A:

Q: Find the integral. (Use C for the constant of integration.) t (294 - t2)3/2 dt

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: To evaluate the integral by making the given substitution

Q: Evaluate the following integrals (from A to E) A. Integration by parts cos dz i) (3t + t?) sin(2t)…

A:

Q: Interchange the order of integration and evaluate the resulting definite integral: cx=1 Cy=1 2³ sin…

A:

Q: how to solve problem in photo attached

A: Substitute x = t2 in the given integral and so the limit varies pi/2 to pi.

Q: Use the substitution technique to determine the following integrals:

A: Important integrals for the question: ∫sec2 x dx = tan x + c ∫un du = un+1/(n+1) + c Other important…

Q: Use the value of the first integral I to evaluate the two given integrals.

A:

Q: Use numerical integration to evaluate the following: dx (b) e-" sin y dy 2 x(x + 2)

A:

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: Reverse the order of integration and evaluate the following integral. 2ex2 dx dy 1 c1

A:

Q: Use the substitution technique to determine the following integrals:

A:

Q: Find the integral. (Use C for the constant of integration.) (t + 3)cos t2 + 6t) dt

A: Consider t + 3 as u. Then,

Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin?(t) cos“(t) dt

A:

Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: To evaluate the integral dx, we substitute x = 2 sec 0. VAx-4 Select one: a. True b. None of these…

A:

Q: Reverse the order of integration and then evaluate. a. S S, x² sin(xy)dxdy

A:

Q: To find the definite integral Vx2 + 64 dx, apply the basic integration rule. Let u = x2 + 64.…

A: We have to find the definite integral. Here we are using integration by substitution.

Q: Evaluate the integrals a) 1 i (y _X dy dx

A: *As per bartleby guidelines we are allowed to answer only 1 question at a time.Please re-post other…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x²V…

A:

Q: Apply the method of substitution to integrate the following integrals: dx I = ; a. Va²-x² b. I = [(1…

A:

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A:

Q: Interchange the order of integration and evaluate the resulting definite integral: cx=1 ry=l a³ sin…

A: According to the limits of integration of the given integral, the region of integration is:…

Q: Find the following integrals using the method of substitution. t2 dt /6+t3 x2 b) J ; dx 5x3+8

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Só S(x?y – xy²)dxdy -2 4/2y, 0 Jy3

A: The given integral is ∫02∫y342y x2y-xy2 dx dy We have to solve this integral by changing the order…

Q: Evaluate the integral. (Use C for the constant of integration.) | 9t sin?(t) dt

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A: To find: The integral ∫dt1-7t6. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C

Q: Evaluate the integral. (Use C for the constant of integration.) x³ + 9x² + 2x + 9 dx T Tx? + 1)(x² +…

A:

Q: Use integration by parts to find the integral. (Use C for the constant of integration.

A: It is required to solve the integration by parts:

Q: Use the value of the first integral I to evaluate the two given integrals.

A: ∫01x3-2x dx=-34

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.