1/30 15x e cosh (15x) dx. Determine J= (Hint: You should not compute the integral by parts. Use the definition of the hyperbolic cosine function instead.)

Q: I. Evaluate the following integrals. Check by differentiation. sin y dy cos²y

A: Given: ∫sinycos2ydy

Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

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Q: V2y? – 3 dy y?

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Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: sin(6x) Vi? +4 dt 7

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Q: 3 9-x 1 dy dx dz V9-2? (x² + y²)1/2 3

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Q: aluate the integral by first reversin TE: Enter the exact answer. dx dy

A: Sketch the region of integration according to the given limits of integration- 0≤y≤9,y≤x≤3

Q: Express the integral a.e •e²² dx in terms of the integral dx .

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Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx…

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Q: Evaluate the following improper integral. If it diverges, then type DNE. Otherwise, find its exact…

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Q: 4 3 b. J 20(2x + 1)°dx 1

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Q: c) Evaluate the following Integration by parts for definite integrals. -5x dx хе 3 ii) . 2 Sin-dx i)…

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Q: Find a bound for the error in the approximation M20 to the given integral (but do not calculate…

A: The given integral is ∫0π35cos(x)dx. To find the bound in error use the midpoint  rule which is…

Q: Suppose a strange particle travels with a velocity (m/sec) of v(t) = , where t is the time it has…

A: velocity v(t)=1t+1 find the travel between t=1 and t=2

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

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Q: Q2 - Evaluate the following integrals i. S cosx sin*x dx

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Q: dx e2a +5

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Q: Use the value of the first integral I to evaluate the two given integrals.

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Q: Q3: Find the integral for the following functions: - 1 dx 1)S- Vx2-2x+1 2) S 3cotx csc² (x)dx 3)…

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

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Q: Set up an integral to find the length of the curve defined by y = 4x2 – 3 from x = 3 to x = 9, then…

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Q: dx a proper or improper integral? Why? (x-3)? .3 Is So 1

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Q: Calculate the integral approximations Te and M6 for f x° dx. Your answers must be accurate to 8…

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Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: Find the indefinite integral.

A: ∫ exex+12dxSubstitute u =ex+1=∫ u2duApply the Power Rule:  ∫xadx=xa+1a+1,    a≠-1=u2+12+1Substitute…

Q: Q2 - Evaluate the following integrals i. S cos5x sin*x dx sinhx dx coshºx

A: See the details solution in below

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

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Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

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

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Q: Q3 Evaluate the following integrals X. cosh? () dx -In2 1 - | 2 - cosh(lnx) dx

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Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: Which of the following integrals is NOT appropriate for a substitution method? Jx'sin(x)dx B S5x…

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Q: 2. Find the following indefinite integrals. (a) / 18z² (b) / 182² dy

A: Integration with respect to x

Q: Estimate the errors in the approximations for T10 and M10 of the integral from 1 to 2 of e1/x dx,…

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Q: Evaluate the integral. (Use C for the constant of integration.) e8θ sin(9θ) dθ

A: Given:     ∫e8θ sin(9θ) dθ

Q: 1- xy dy = 0. 1+ xy

A: 1+xyx2y.dx+1-xyxy2.dy=0 (Now multiply both sides by (x2y2) ): y1+xy.dx+x1-xy.dy=0 or,…

Q: Evaluate the integral ∫e^(2x) sin(e^x) dx, by first making a substitution and then using integration…

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Q: Use Simpson's rule to find the value of the following integral -3x² dx -0.9 e 0.1 where n=4

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Q: Calculate the integral approximations To and M6 for 10 x³ dx. Your answers must be accurate to 8…

A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

Q: ∫ (e3x+5ex+2  divided by  ex) dx a.) Compute the integral

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Q: of the following is an improper integral? • In3e COsx dx xe | in(x*+1) dx n(x++1)dr -4 x2-x- 2

A: Improper integrals are characterised as

Q: | (x" +e – dx x2

A: The objective is to find the value of given integral

Q: Evaluate the following integrals using Integration of Hyperbolic Functions. 14. S sech? ( Inx) dx…

A: Integration is the inverse of differentiation and we are going to use that concept here. Therefore…

Q: Evaluate the integral. (Use C for the constant of integration.) e^−θ cos(3θ) dθ

A: ∫e-θcos3θdθ We need to Evaluate the integral Using C for the constant of integration.

Q: Find the integral for the following functions: - dx 1) . Vx²-2x+1 2) ſ e3se c(x), sec(x). tan(x) dx…

A: Solution: The objective is to find the value of given integral

Q: (d) L™ x³ cos(x* + 5) dx. (e) f(2x – 1)³ dx . -

A: For the given integral  ∫0π4x3cos(x4+π2) dx

Q: Q2 Find the integral for the following : dx 1-S 2Vx+2x 2- Se-*sec² (ne¯*)dx 3- S dx 1+e*

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Q: 1. Approximate the following integrals using the Trapezoidal rule. c0.5 a. dx 1.5 x Inx dx c. 2x dx

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Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

A: The given integral,           ∫015238-38x2dx