Evaluate the integral f (t* In ti+ 3t° sin (t*) j + ) dt. (x+1) -2

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

A:

Q: e In (xle ) (2– sec²x) sec(3A – x) sec³x dr What should be the value of A for to be integrable using…

A: integration by substitution method

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

A: Explained below

Q: Evaluate the integral S (t³ In t ì + 3t³ sin (t*) j + x-2 *(x+1) k) dt.

A: We will use the fact that when we calculate the integral of a vector valued function we integrate…

Q: evaluate the integral. +t In(t“ + 1)j |dt te

A: Given that: ∫01t·e-t2i+tlnt2+1jdt

Q: Determine the fool wing integrals: 1. e2*cos3xdx . 2. J.x² In(x+ 4) dx -

A: Use integration by parts

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: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

A:

Q: Evaluate the integral S (t³ In ti + 3t³ sin (t*) j+ x-2 X(x+1) k) dt.

A: In this question, we have to find the integral of the given vector function. Here we integrate the…

Q: Evaluate the integral.  integral  t 2 sin 2  t dt

A:

Q: Je t ež cos (2t)dt

A:

Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

A:

Q: Evaluate the integrals in Exercises 1. esin (e) dx 2. e cos (3e – 2) dt

A: Given the integration I=∫exsin(ex)dx

Q: In 3 xp; J(1-x)*dx

A: Given,

Q: Evaluate the integrals in Exercises using integration by parts. 3. f cos t dt 4. * sin x dx

A: The formula for an integral ∫udv is uv-∫vdu. Here u function is selected on basis of ILATE order.…

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

A:

Q: tan x dy S dx S 1+y?

A: Explanation of the answer is as follows

Q: Evaluate the integral S (t³ In ti+ 3t sin (t*) j+ ) dt. 1-2 x1)

A:

Q: Evaluate the integral (1+ sin t)' cos t dt using the substitution u = 1+ sin t. (1+ sin t)' cos t dt…

A: Recall: ∫xndx=xn+1n+1+C

Q: Evaluate the integral | t(sec t2)4 dt

A:

Q: Compute the integral 1 dx. L (* – i)(x² + 1)

A:

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Evaluate the integral. integral t e -3t dt

A: Let given integral be - y = ∫t e-3tdtUsing by parts to integrate the above integral - ∫uv dx = u∫v…

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

A:

Q: Evaluate the integral / (4 + + sin t)° cos t dt using the substitution u = 4 + sin t. (4+ sin t)°…

A:

Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

A:

Q: Evaluate the integrals in ∫7cos t sin t dt

A: Given Integral,I=∫7 cos t sin t dt

Q: Find the line integral of F =9xy*ï +(x² + 3),yj over the path L.

A:

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: Compute the integral fo S x cos(xy)dxdy

A:

Q: Evaluate the integral

A:

Q: evaluate integral of Ś t^2 ln(t) dt

A:

Q: Evaluate the integral. "π/4 J.T tan (0) sec²(0) de

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

Q: Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with…

A: The Maclaurin series: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at a=0 or x=0. Given:…

Q: Evaluate the iterated integral. TT- 9x 3x2 sin(y) dy dz dx

A: The objective is to evaluate the iterated integral.

Q: Find the integral of (t^2 sin(t)cos(t) + t sin^2 (t) )dt

A: We have I=∫t2sin2t+t2costsintdt

Q: Evaluate the integral. (Use C for the constant of integration.) t2 dt 1 - t6

A:

Q: Evaluate the integral S (* In ti+ 3t sin (t*) j+ k) dt. x(*+1)

A:

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: Evaluate the integrals in Exercises 1–6. (sin¬l x)² dx 1. dx 2. x(x + 1)(x + 2)· . · (x + m) 1 /sin'…

A:

Q: Find the general indefinite integral using definition. (3t*-t³+6t²\ a) dt b) S(3 sin x – 4e* + 5* +…

A: Part a,Given,          ∫3t4-t3+6t2t4dt

Q: Evaluate the line integral along the curve C. S-s - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O…

A:

Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

A:

Q: The result of the integral in 0 given V Vr²- 25 -dy is 5 tan0 -50 +C, True B False

A:

Q: Find the total differential. z = e4x sin(3y) dz =

A:

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α<1 b)α>1

Q: . Evaluate the integral S (t* In ti+ 3t sin (t*) j+ ) dt. +1)

A:

Q: Find the integral of f (z2 +x2 + y33) dt.

A: Given : ∫z2+x2+y33dt