Given a 6t+34 and y 21f2 +122 dx (i) dt (ii) .(write the simplified answer) ||

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A: Given the integral ∫dxx24x4+932 We will use the the method of substitution to evaluate the integral.

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A:

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A: Differential equations

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Q: Evaluate: dr 3x?++C 4 A B +C 3x3 3x2+ +C 4x3 +

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Q: x dx Evaluate (4a² +9x?) 2

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Q: 3 2. x1 + x² dx

A: Definate integration

Q: g(x.y)-xn (x-y), as(-2,3) Pind vg ?

A: Given the given function is gx,y=xlnx+y,    x,y=-2,3. Apply gradient formula ∇f=∂f∂xi+∂f∂yj

Q: Explain how the three formulas a. d dx (xn) = nxn-1 b. d dx(cu) = c du dxc. d dx(u1 + u2 + g+ un)…

A: a)ddxxn=nxn-1b)ddx(cu)=cdudxc)ddxu1+u2+....+un=du1dx+du2dx+....+dundx

Q: d [(5 – 3x – 4x³)5(3x – 4)] dx

A: Derivative using product rule.

Q: 2 с. dx

A: topic - definite integration

Q: S 2x/6-7x dx 6.

A: Using substitution method.

Q: Evaluate:

A: Given

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A:

Q: S7=1−1/√2+1/2−12/√2+14−14/√2+1/8.

A: Given:

Q: d 18x 5. In(9x? – 8) : dx 9x2 – 8

A: Consider the following expression: ddxln9x2-8 Apply the chain rule:…

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A: Given, ∫x1.3+7x2.5dx  We have to find the integral.

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Q: - 49 -dx = X (Type an expression using x as the variable.)

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Q: 7x dx 19. (1 – x²)3

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Q: 1 5- x + 3 2. Va dx Find - x6

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A: Given : ddx1+2x2