check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the sum so y"ty= %3D

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A:

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A: To verify: The integration formula, Formula used:

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A: We have to solve

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A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

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A: we have to find definite integral of f(x) in [0,pi/2]

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

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A: To evaluate ∫sech x dx

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A: We have to prove that the given integral is true.

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A: This integral can be solved by the method of substitution.

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A: Consider the following: Differentiating the function with respect to x on both sides, we have,

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A: Integral of the given function is -

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Q: (A very cute proof ) I want you to show using integration by parts that sin(mx) sin(nx) dx = 0 if m…

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A: Solution is in step 2

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A: Using differentiation of   product rule and implicit differentiation,

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Q: 3. Find the equation of the tangent line to sin- (x – 2y) = 2xy- 1 at the point ( 1, ;).

A: We will solve the problem