Use the identity f(x) dx = f(x) dx + f(x) dx to compute the integral. %3D -A -A sin(t) dt (Hint: sin(-t) = -sin(t)) 1 + t2

Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy dx

A: Given: ∫-40∫x+42x+4siny3-3y2dydx To do: Evaluate the given double integral.

Q: Evaluate the iterated integral. 5 sin(x + 6y) dy dx

A:

Q: Integration in REVERSE ORDER

A: Given:

Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

A:

Q: Evaluate the iterated integral: xy'e-" dx dy

A: Here we evaluate the iterated integral

Q: Evaluate the integrals: V2 1- dx (T/2 7cost sin t dt 2-

A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

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

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Q: Evaluate the iterated integral: 2 sin(xy) dy dx п/2 1

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Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: Evaluate the given integral 2x +3 -dx- (x + 1) (x – 1)²

A: Integration formulas help to integrate the given fuction. Simplification of the function helps to…

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: Evaluate the iterated integral. 74 (x² - 2y²) dx dy

A: Given that a double integral we solve this integration by using general property of integration.…

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: Evaluate the double integral: sin(y) /y³ dy dx.

A: Change the order of integration to simplify the integral .               Disclaimer: Since you have…

Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

A:

Q: Solve the integral equation F(x) cos px dx =. [1-p,0sp 1.

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

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: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

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

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Q: x-3 dx r³+9x +9.x

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Q: Evaluate the iterated integral. V1- x8 dy dx

A: We have to find

Q: Evaluate the integral sin (y²) dy dx.

A: The given problem is to evaluate the double integral, we have to change the order of integration and…

Q: Evaluate the integral with the order reversed. dx dy -2 0

A:

Q: Find the integral. (Use C for the constant of integration.) [(++ 3)cos( 2 + 6t) at (t + 3)cos( t2…

A: To find the integral

Q: Find the most general antiderivative (a) Integral [ (cos(ln x)) / x ] dx (b) Integral [ (x2)(ex^3)…

A: Given (a) ∫coslnxxdx  (b) ∫x2ex3dx  We have to find the most general antiderivative.

Q: Find the integral of dx V1 – x²

A: Solve by integration

Q: 1. S √x dx VX +1

A:

Q: Solve the integral: dy dx. x2 H/4

A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

Q: Evaluate the Integral dx 4. S V1-e-2x

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Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: TX Evaluate the integral dx dy by reversing the order of integration. 2 Cos 0.

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: • Evaluat the integral:- 푼 S S. seč (cosx) dx dy Sin y

A:

Q: Evaluate the iterated integral. 4 (x2 – 2y²) dx dy

A: Given problem:-

Q: evaluate the given integral.

A: Solution:-The given integral is  ∫x+2(x-1)(x+3)dx since  x+2(x-1)(x+3) is solved by partial…

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

A: The given integral is:∫-2x+4x2+1x-1dxWe need to evaluate the above integral.

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

A:

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

Q: Find the integral by Integration By Parts. 2. 0 cos r0 de 3. cos t dt 4. x² sin x dx

A: Integrating By Parts Rule.

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Change the order of integration. "A/2 x + 1 3 sin(x) dy dx

A: Consider the graph:

Q: [2'e'dx X

A: Given

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

A: