.3 1+ at dt

Q: 7/2 sec*(t/2) dt

A: Here we will solve the given definite integral,

Q: 7.S dt J VE+2- 5

A:

Q: 3. Evaluate J (2x + 5)(x + 5x)'dx.

A: The given integral is ∫2x+5x2+5x7dx

Q: SVA 1. dt 1

A:

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: -dt (t+1)ª (t–1)*

A: Solution

Q: 12 (4x – 5y) dy dx

A:

Q: Evaluate the integral: √ S - (9x²+7x) (x−1)(x+1)² dx = ← +C

A: Given; I=∫-9x2+7xx-1x+12dx   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 7) Evaluate: S(-x² + 4x – 1)dx

A:

Q: ху + (1 + х) у %3D ех ex

A: Answer and explanation is given below

Q: Evaluate the integral : S 8г2 +10х—6 (х—1) (х+1)2 dx = |

A: The given integral is ∫8x2+10x-6x-1x+12dx.

Q: (b). Evaluate the integral 6x Vx +4 dx.

A: Part(b) Given

Q: 6. f(x, у) — х3 In (2y)

A:

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

A: Taking substitution as 2x+1 = t

Q: Evaluate S (2x+3) dx x² (x²+1)

A:

Q: [ -1 + dt X2 with x1(0) = 1 and x2(0) = –1.

A:

Q: ,3 In x dx

A: Solution

Q: d 1) Find sec dt 2)

A:

Q: 2. S dt

A:

Q: 1. [8e" dt

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: 6 S(3csc°C+) - &e*)dt

A: Given integration is : ∫3 cosec2t-8et dt To find the value of integration

Q: 10e. Integrate F (1) dt

A: Given that rt→=t+1,t,1t.

Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: 32x ) dx In|xl + C 3 %3D - |- 3x. 2 In 3

A: let the missing term is Y

Q: 3. Evaluate the integral fx?x* + 4x + 3) dx

A:

Q: Find the indefinite integral. dx (x+4 3/2 +C 4x2+4 +C 4x2+4 + C 4x+4 4x +C

A:

Q: 9. 23/2 3√x+1 - S dx

A:

Q: 1. F(s) = 2)

A:

Q: Evaluate e dt 0.2

A: We have to use standard gamma integration here.

Q: ) dt 5e + 1+ t2

A: Take the help from standard form of integration and simplify.

Q: Calculate S√4-x² dx

A:

Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

A: The objective is to show that ∫-∞∞ x2x4+x2+1dx=π3

Q: ()* 3 -2 dx 7. dt 4

A: Solution 7: Given linear system is dxdt=3-24-1x Let A=3-24-1 Let the eigen value be λ So…

Q: 3.53 dx Compute 3+9,2

A: I=∫013313+9x2dx=19∫01331x2+13dx=19∫01331x2+132dx Since, ∫1x2+a2dx=tan-1xa

Q: 6x+3 J x+sx +6

A:

Q: Evaluate 4 1 2 (Nat 13.402 - -13.402 13.042 • Vx + 3 3 X 4 | -13.420 +18 -1.3204 4 X None of them 4…

A:

Q: Compute S 4(x)dx for 4 X<1 %3D

A:

Q: Evaluate Ssin" (2sv1-x*)ds. dx.

A:

Q: find the derivative.

A: On simplification, we get

Q: 1. Evaluate [(2sin 2x+3Tanx – 5 e-5* +4x' -7) dx .

A: Integrate each term

Q: | 3tan-1(x)dx = %3D 2프-21n2 In(4) 2/3 None 을 + m2 2 In(÷) | 3 3 - In(4) 6 3

A: Solve by parts method of integration.

Q: 21. 1dx dy -3

A:

Q: Suppose A = 500(1.045)t . Compute dA/dt

A: Given function: A=5001.045t We have to find dAdt. Differentiate the given function w.r.t 't'…

Q: Show that 5x – 2 3 + C X - 1 dx = 5 In |x - 1| x2 – 2x + 1

A: We have to solve

Q: Inx dx

A: Substitute Ln(x) = t and use integration by parts.

Q: 1 2, 1)dt '1+t calculate

A:

Q: 7. Evaluate the integral x4 6x5 1 dx

A:

Q: Compute x1+ x² dx 3

A: Given,           ∫01x1+x23dx

Q: Evaluate the following integral. 8 4-2y/3 12- 2y – 3z 1 dx dz dy 1 0

A: To solve I=∫18∫04-2y3∫012-2y-3z1ydxdzdy