Oz= 0 )x = 0 Oy=0

Q: 3) | (1– cos² 2t) dt (Trigonometric int.)

A: ∫0π(1-cos22t)32dt

Q: Ju

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A:

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A: Sin(A+B)=sinAcosB+sinBcosA

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A:

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A: Given that a baseball is thrown with an initial velocity of 110 m/sec atangle of 30 degrees above…

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A: To prove : sinθ1+cosθ+1+cosθsinθ=2cscθ

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A:

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

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A: Topic = Integration

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A:

Q: In ab 1+ In² y [tan-1 (In y)]dy

A: Given, I=∫lnab1+ln2y1y[tan-1(lny)]dy Take Constant out, as∫af(y)dy=a∫f(y)dy…

Q: 19. y = -3 cos 2x 20. y = 5 sin 2 AAMA A

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: We are given the integral: ∫a22a1sin 3z+a coth 2zdz Let I=∫a22a1sin 3z+a coth 2zdz I =∫a22a1sin 3z+a…

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A: Euler’s Theorem is a generalization of Fermat’s little theorem dealing with powers of integers…

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

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A: 37) The value of u in the given integral is assigned and the integral is evaluated as follows.

Q: use in tergration by parts to solve

A: Given,  ∫012xcosπxdx  We have to find the integral using integration by parts.

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: For direct Proof:

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A:

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5

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A:

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

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A:

Q: 8. eeer +eyty dy

A:

Q: Evaluate the integrals

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A:

Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

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Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: .3 4 cos³ 4y /sin 4y dy

A: To find out the integration.

Q: using Trgananetre Represent the Fonrier Selies 1 fex) ○くxく1 -1 -1 (x 40

A:

Q: Ho = 0,~Po(x) = { 3 otherwise Hz = 0,~p1(x) = 1 Osxs1 O otherwise

A: It is an important part of statistics . It is widely used.

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

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Q: y Newton-Raphson method to fin

A: Given: f(x)=x2 cosx2+sinx cosx To find: The root of the given function by applying the…

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A: Solution:-

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A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

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Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

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A:

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A: