s(t) = 40 sin 2t at t = 0

Q: =D{sinh(2r) – ţa dy/dx agi

A: We know that sinhx' = coshxx' = 1 and (f(g(x))' = f'(g(x))g'(x)

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

A:

Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

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Q: // sin(7x²) dx dy. Compute O y/3

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Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

A:

Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

A:

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: find dy/dx if y = sin-1(1/x)

A: Here given as

Q: ∫(3t+t²)sin⁡(2t)dt

A: Given that, the integral is ∫3t+t2sit2tdt.…

Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

A:

Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

Q: /2 (e) [™¹², sin(x) cos(x)dx

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Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

A:

Q: Let y tan(4x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when x…

A: Given : y = tan(4x + 6)   To find the differential dy when x = 5 and dx = 0.2 Also to find the…

Q: 1. еat sin mx dx 0. 8.

A: Given data: The given integral is I=∫0∞eatsin mxdx. The given integral can be written as,…

Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

A:

Q: 211 sin nx dx [ [1-cos2nx]dx t, where n %3D

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Q: Find the differential of the function. y = 0 sin(60) dy =

A: To find the differentiable of the below function. y=θ3sin6θ

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A:

Q: Let y = tan(3r + 5). Find the differential dy when x = 3 and da = 0.1 Find the differential dy when…

A: Here we need to use chain rule of differentiation to find dy. According to chain rule,…

Q: find dy/dx if y = (sin-1 x)2

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Q: Find dy/dx of y sin -1). A 3. B 1-9r2 D

A: Y= sin-1(1/x)  and we have to find dy/dx

Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

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Q: d. t sin 2 dt COS dx 3

A:

Q: a(22) V17 – cos(2nt)" (2 – 4) sin() 1. Given f(x) dt, find the equation of the line tangent to the…

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Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: find dy/dt. y = sin2 (πt - 2)

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Q: dx/dy + sin'3 y/ cos'2 2x = 0

A: We are given : dxdy+sin3ycos22x=0⇒dxdy=-sin3ycos22x⇒cos22x dx=-sin3y dy Integrating both sides, we…

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: sint In(cos t)dt

A:

Q: Let y tan(4x + 8). Find the differential dy when x 5 and dx = 0.2 Find the differential dy when x =…

A: Topic = Derivative As per guidelines , At a time only one question can be answered.   use formulalet…

Q: 4. § xe¯ dx 6. |t sin 2t dt Jx² cos mx dx 8.

A:

Q: Let y = tan(4r + 8). Find the differential dy when a = 4 and da = 0.3 Find the differential dy when…

A: Differential equation: - A differential equation is an equation that contains the derivative of an…

Q: a. cos x dy + y(sin x - 1) dx = 0; when x = 7, y = -2

A: According to our guideline we are supposed to to do only the first question if you want any…

Q: 3.1.1 L sinh 3t dt

A: The Laplace transform can be obtained using the table of the transforms. The integral for the…

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: Find dy of the function y = cos2 3X + √√Sin x dx

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Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: Find the differential of the function. y = 6 sin(60) dy

A:

Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: 1.) dx = t (1 + t2) sec?x dt ans: 2x + sin2x = (1+ t?)² + c

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: Find (dy)/(dx) if ey = ex + sin(x2x).

A: Given ey=ex+sinx2x

Q: Let y = tan(3x + 5). Find the differential dy when a = 4 and dæ = 0.1 Find the differential dy when…

A:

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

A:

Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.