D. ( [ 3° cos"(5t) dt sin(z)

Q: e (a cos bx + b sin bx) a + b? ax Secos bx dx=-

A:

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: Cos“ 2t osh wt sin wt e2t sint

A:

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: Find dy/dx and d2y/dx2. x = 8? + cos ?,    y = 9? − sin ?

A:

Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: -을 x e [T, 3 J Sinx =

A:

Q: j) S (2 cos a – e) dx

A:

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: d. 3) [cos πx]4 %3D dx

A: 3) To find the derivative

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

A:

Q: 0 16) cos t dt dx

A: Given:

Q: 1. cos? 2t dt

A: Given query is to eveluate the integral.

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: | dy cos(t?) dt, then what is =? If y = COS dx

A: Given,          y=∫xx3cost2dtWe know that,          From the funcdamental theorem of calculus, we…

Q: •T/2 cos“ x dx. OS

A:

Q: d 27. dx ], cos t dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: T/2 cos t dt 1 + sin²t

A:

Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: dy If x = a (0 – sin 0), y= a (1– cos 0), then find dx |

A: Introduction :

Q: (b) I cos cos(√x + 3) dx

A: b Given integral is ∫cosx+3dx. We have to solve the given integral. Use formula…

Q: The result of dy/dx for the following function is COS X y = 1+sin x

A:

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: Find dg(t)/dt -1 1+ cos t g (1) = %3D sin t

A:

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

A:

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: Find dy : (a) y = cos(1 Ix + 5x) dx

A: Topic:- calculus

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

A:

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

A:

Q: L(cos at) = %3D s2 - a2 صواب İhi O

A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

Q: T For y 10 cos ( 10x 4 - its amplitude is its period is its phase shift is

A:

Q: d. t sin 2 dt COS dx 3

A:

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

A:

Q: find dy for ee Sin (メ+34) dx

A:

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

A:

Q: The general solution of the DE dx dy = cos?y is

A:

Q: dy = sin (t) and x= cos (5t-2), hence find dx Given that y 3=

A:

Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: b) ſ cos (Inx)dx=?

A:

Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

A:

Q: evaluate the triple iterated integral.

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Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: Find dg(t)/dt 1+ cos t -1 8 (1) = sin t

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Q: d Cvaluate dx cos (r² + 1) dt

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Q: COS T dx sin' a

A: given that a integration we solve by using integration method . Here i attached solution of this…