dz Given z = 4x? + y²,x = sin t, y = t², find - dt

Q: Find the R.M.S. value of xe* as x varies fromx =1 to x = 3.

A: The given data is: To find the R.M.S value of xex as x varies from x=1 to x=3

Q: dx 5x. J 75V9x² – 1

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Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

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Q: y = secx means where x and sys

A: Given, y=sec-1x

Q: dy +Zy =0 du

A: Given: dydx+2y=0   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where 'a' is the constant.…

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: Differentiate the function y= 1-ex #48 y= e + Sincee) Cin2x

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Q: r=secxcscsx dr/dx=

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Q: x dx 1o. 8 x-X

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Q: sec²x dx V 5 - sec2x

A: Given that the integral  I = ∫sec2x5-sec2xdx let sec2 x = tan2x + 1 I = ∫sec2x5-tan2x+1dxI =…

Q: Differentiate implicitly to find d2y/dx2.   3y2−xy+5x2=5

A: Differentiate implicitly to find d2y/dx2.  3y^2−xy+5x^2=5

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: dy Find dx2 18x? + y? = 7

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Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: -dx x +1 2 5.

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Q: Find y in terms of x given that (1+ x) = x²y and that y = 2 when x = 1. dx

A: The given differential equation can be simplified as shown below: (1+x)dydx=x2y     ⇒…

Q: dx 7. 7- Зх

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Q: 3. Evaluate ry? dz dr dy.

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Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

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Q: Find dy when r + y? = 5.

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