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Q: Find the antiderivative of 5sin x In5 cos x dx 5coS x + C 5sin x In 5 + C O sin x + C In 5 5sin x +…

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Q: The Fourier sine integral of S(x)=- 0, 2, 0<x<3 is 0 <x O a. 4 sin(3@) sin(@x) do Ob. 4…

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Q: ,3 Evaluate the iterated integral dx dy

A: We have to evaluate the iterated integral ∫12∫yy3dx dy.

Q: expand e cos y near (17) 1, by Taylor's Serios method

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Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: (b) Find the Fourier cosine and sine integrals of f (x) = e¬kx, for x > 0, k > 0. %3D

A: Solution of the problem as follows

Q: Evaluate the integral. ∫0pi 9sin^2(t)*cos^4(t) dt

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 1. Evaluate the following integral: (1-e-²x) dx (a) analytically;

A: Note:- For this problem all the sub-parts  are different as methods are different. So, we can solve…

Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

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Q: 2. (a) | +4 Evaluate the integral. √2x + 1 dx

A: Taking substitution as 2x+1 = t

Q: The integral 2n / 14xe dx can be done with the substitution u - and du= dx.

A: Step 3Given,2π∫14xe-x2dx

Q: (c.) Evaluate the integral [xV2x +1 dx ?

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Q: Evaluate the integral: Jo Sí(3xyY+ 5) dy dx Answer:

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Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫2x(x2 + 5)-4 dx, u = x2 + 5

A: Consider the given integral: ∫2xx2+5-4dx=∫2xx2+5dx-∫4dx Substitute u=x2+5→du=2xdx in the above…

Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

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Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

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Q: Find cosh a In(sinh r)dr.

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Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: a) I = [ In(1+x²)dx

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Q: Evaluate the integral: el/z dx -1

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Q: 15+0. The improper integral e* dx is

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Q: Tind dʻz of z- In (xy) Find d²z z - In (xy)

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Q: 2 1 e dx e

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Q: 1 |Using u-substitution we find that In(2x + 1) dx In?(3) 2x + 1 JO

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Q: For O S O 1/2 dx and using the substitution 1/2, the resulting integral takes the form: U=X U du -du…

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Q: Consider how we can evaluate this integral using u-substitution: x S dx. √2x+1 If we let u = 2x+1,…

A: This question can be solved by integration by substitution.

Q: dx Integrate: J. 3n B. A. EIN

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Q: Find cosh r In(sinh a)dr.

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Q: following integrals 3 a) Evaluate IT2-4xy+4y² dxdy=? 0, 0.

A: Given that the double integral To find evaluate the double integral

Q: In evaluating z(4– 2)šdx,if we use the substitution that u = 4– 2, then what will be the resulting…

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Q: S- S- °S- S For x 1/2 x- U U 1-u4 4u dx and using the substitution -du -du -du 4u √4-(24²) 2 -du…

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Q: Consider the integral 3e 2 dx . Using u-substitution, what is the appropriate u and du? 2e -2r A u…

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Q: (4) Evaluate the iterated integral ". Scos" 3r² sin 0 dr d0.

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Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: Q2 Show that the region included between the cardioids r=a (1+ cos 0) r = a (1- cos 0) is given by:…

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Q: The integral 2N | 6xe- dx can be done with the substitution u = and du = dx.

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Q: Which of the following is NOT true about the DE: 6x²ydx +2x*dy=0?

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Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

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Q: II cos(s5) dt ds

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Q: 1. Find b such that |(a) In 3. dx is equal to х (Б) 3.

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Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

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Q: The value of f(z) = Ln z at z = 4 + 4i in terms of x+ iy is %3D Oa. In 8+i- 4. O b. In 32+i la 32+1…

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Q: 3. It is known that e dx e - e. Use this result to evaluate the following integral: 3 e+1.4dx %3D

A: Given, ∫13exdx = e3 -e   Using the above result, we have to find ∫13ex+1.4dx

Q: (e) 1 sinh z +25 n=1 (-1)" z *2 + n2π2

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

A: