Evaluate the following definite integrals. Show all the calculations. V2 s²+V5 ds 2.1 s2 V3 2.2 Lt + 1)(t?+ 4) dt

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A: Q 1. Consider the definite integrals: ∫043x-x24dx To solve the given integrals: ∫043x-x24dx=∫043x…

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Q: V Sx² +4 dx

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Q: Q2 – Evaluate the following integrals- S cosh(2ln(x))dx V.

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Q: Evaluate the following integrals. Show all the necessary solutions. 2. y In?(1 + 3*) dy 1 + y²

A: I=∫y ln7(1+y2)(1+y2) dyI=∫ y ln(1+y2)7(1+y2) dyln(1+y2)=t1(1+y2) (2y) dy =dty(1+y2) dy=dt2

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Q: Evaluate the following integral -1.6 Ax? + Bx + C + 5 dp- I = sin 2x (i) Trapezoidal Rule (ii)…

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Q: 5e2*dx V9e4* – 6e2* + 1 (A 3e2 (B 3e2x – 2 3e 2x – 1 9e* – 6 + 1 e 2x _ E) None

A: Solved below

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Q: Q2 - Evaluate the following integrals i. x cosh(x² + 1) dx -0.5

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Evaluate the following Integral by using suitable method: 2y3 +y y4 + y² + 1' ª |7 +e-4y . -) dy

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Q: 6.) | dx 4 – x²

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Q: Evaluate the given definite integral using appropriate substitution: 8e2a dx @ 4e4 – 4 A © 4e4 + 4…

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Q: Evaluate the following definite integrals: (a) Si (Vi – %) dt (t+1' dt (b) t3 -3 (c) Sm (et – e-t)…

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Q: Evaluate the following integrals by first reversing the order of integration. 8 2 √° ²₂ √² + 1 dr dy…

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Q: T6 Based on the image attached, differentiate each of the following integrals with respect to x.

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Q: Q4 Evaluate the following integrals cosh? (=) dx -In2 1 - fe 2 - cosh(lnx) dx

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Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

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Q: 1 8.) / dx (x2 + 16)3/2

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A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

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A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: ܐܐ 19. dz 'z(nz5

A: The given definite integral is ∫122 dzzlnz1/5. Solve the definite integral by the substitution…

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Q: S(e-³y V5 + e-3y 2y³+y -)dy зу - y4+y2+1

A: Given,

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Q: 25. Evaluate the following definite integrals. e) L, 3wv4 – w2 dw

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Q: Evaluate the following integrals. Show your complete solution. 2 dy 1. S Зу-4 2. S dv v+3

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Q: Evaluate the following integrals using power formula. 1) S3t dt 2) dy 3) S(5x* -8x³ +9x2 - 2x + 10)…

A: We have to evaluate the following integrals using the power formula. 1. ∫3t6dt2. ∫1y3dy3.…

Q: Evaluate the given definite integral using appropriate substitution:8 8e2 dr -4e4 + 4 ... 4e4 – 4…

A: We have to solve the problem

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 definite integral below. -10r i+16r' j+8t k dt

A: ∫12-10t4 i+16t3 j+8t k dt

Q: S÷t cos 4t2 dt 2 4r dr (1-r2)7

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Q: / FVA 12.) dx x²/25 – a²

A: Given integral is ∫1x225-x2dx Substitute x=5costdx=-5sintdt

Q: Q3/ Use Simpson's (1/3) Rule to evaluate the following integrals, Assume (h=1)? sicx³ + x² – 5) dx

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Q: Evaluate the following Integral by using suitable method S(e-4YV1+ e-4y 2y3+y dy y4+y2+1/

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Q: 1 dx x2 (1) x=1 x=1 (2) et dx x=-0 x=-∞

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Q: 2 s² +V5 ds 2.1 s2 V3 L(t + 1)(t2 + 4) dt 2.2

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Q: Evaluate the following definite integrals. (a) | |2t – 4| dt. T/6 (b) cos(3x) dx. e (c) dx.

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Q: 2. dx

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Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus. s 49 – s2 ds =…

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Q: Find the complete integral of the following equation PDE By charpit's pq+2y(x+1)p+x(x+2)q-2(x+1)=0

A: Given : The equation of the PDE is : pq+2y(x+1)p+x(x+2)q-2(x+1)=0…