7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by sechx sechx

Q: Use a calculator to compute sinhx and coshx for x = -3, 0, 5.

A: We use a calculator to find the values.

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A:

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A: The integral is . Let . Differentiating both sides.

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A: Find the integral

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A:

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A:

Q: sin 3x dx 3-10cos3x 10.

A:

Q: 2sinh cosh -dx 3cosh? * 2

A:

Q: Simplify (2æ* yz*) · (5a²y*z) 10x14 ,5 y* z' 10x°y³ z4 7x° 7x^6y*3z^4 7x° y* z 4,5

A: We have to simplify the given function, (2x3yz4) • (5x2y3z)

Q: Find a suitable substitution for evaluating ∫tan x sec2 x dx andexplain your choice.

A: we have to integrate the following integral using a suitable substitution. ∫tanx.sec2xdx

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A: ∫Axndx =A(xn+1n+1)+C, where C is integration constant.

Q: Lion 1-y If x = Show that 1+y dy V1-y

A:

Q: Stan³ x secx dx

A:

Q: Find 6x2 sin x3 dx

A:

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A:

Q: Differentiate, hcx) = In (x-Vr

A:

Q: tanxsinx + cosx = secx

A: tanx sinx+cosx=sinxcosx·sinx+cosx   ∵tanx=sinxcosx=sin2xcosx+cosx=sin2x+cos2xcosx=1cosx…

Q: @) find 16+9X 2

A: Question (1) - Let the given integral be y - y = ∫043 316+9x2dx          Taking 9 common from…

Q: 6/T-9x dx

A: Here we have to integrate        ∫[(6√x - 9x)/x2] dx