gral can be parametrized using Feynman inte -x cos(tx) dx, where t = 4, and I(0) = e dx = 0. ming differentiation under the integral sig d substituting the limits, we now have: |(t)

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A: We have to find

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A: Use substitution tan(4x)=t

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A:

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A: Use the change of order of integration to solve this problem.

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A:

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A: ∫-4y3 dy

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A:

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A:

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A:

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A:

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Q: 12) S (z* + 2x + 1) dx 3 х2 + 2х +

A: Integration

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A:

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A:

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A:

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A:

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A:

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

A:

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

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A:

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A:

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: We have to solve

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A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

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A:

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A: topic - indefinite integral

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A:

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A:

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A: Put value in  given  integral

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A: Given,            ∫7tan xlncos x dx

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A:

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A: Topic- integration

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A:

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A:

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A:

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A:

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Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

A: