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#### DeusAbscondus

##### Active member

- Jun 30, 2012

- 176

Find the area under curve $y=243x^5$ and between y=1 and y=32

Here is my working out:

1. transpose to make x the subject

$$x=\frac{y^{1/5}}{3}$$

2. integrate in y

$$\int^{32}_1 \frac{y^{1/5}}{3}\cdot dy=(\frac{5\cdot 32^{6/5}}{18})-(\frac{5}{18})=17.5$$

Which is discrepant with given solution of 157.5

Question 1:

Would someone kindly check my answer as I'm beginning to suspect that I have been detained for hours by an error in the solution (ie: $157.5$ could be $17.5$ with a careless interpolation of $5$ between first 2 digits of my answer)?

Question 2: How could one have rewritten the original function so as to translate its curve by 90 degrees and integrate along the x-axis?

Thanks kindly for any help you can offer.

Deus Abs

Here is my working out:

1. transpose to make x the subject

$$x=\frac{y^{1/5}}{3}$$

2. integrate in y

$$\int^{32}_1 \frac{y^{1/5}}{3}\cdot dy=(\frac{5\cdot 32^{6/5}}{18})-(\frac{5}{18})=17.5$$

Which is discrepant with given solution of 157.5

Question 1:

Would someone kindly check my answer as I'm beginning to suspect that I have been detained for hours by an error in the solution (ie: $157.5$ could be $17.5$ with a careless interpolation of $5$ between first 2 digits of my answer)?

Question 2: How could one have rewritten the original function so as to translate its curve by 90 degrees and integrate along the x-axis?

Thanks kindly for any help you can offer.

Deus Abs

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