Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I V1+ (2z + 2)ďæ B + (2x + 2)²dx 5 1+ (æ² + 2æ)°dæ

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A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

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A: The given series is: ∑n=1∞(-1)n+12n+2n3+n2+n Now, let  an=(-1)n+1(2n+2)n3+n2+n & bn=nn3=1n32-1=1...

Q: Original Integral Rewrite Integrate Simplify 9 dx dx 9 + C (4x)5 1024 1024

A: Topic = Integration

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A: Solution is here

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A: Solving the differential equation by seperation of variables

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A: We can evaluate the answer as below.

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A: As you mention question no. 6 solved

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A: Let's find. 

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A: Here we check the convergence of the given Integral.

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A: We have to find the values of x and y.

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A: Given, P = &lt;3, 4, 4&gt; and Q = &lt;0, -2, -5&gt;  

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Q: Evaluate the function y = - for x = 3 to x = 5 in steps of 0.5. Write the complete x+ code

A: % Matlab Code% defining the range for xx = 3:0.5:5;y = (x) ./ (x+(1./x.^2))

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A: We know, (i) ∫dxx2-a2=12alogx-ax+a+C, C is a constant.

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A: This question is based on differential equation.