Maths Ext help (1 Viewer)

cossine · Jun 22, 2022

So the integrand is area of the cross section. So just integrate that.

5uckerberg · Jun 22, 2022

Farhanthestudent005 said:
View attachment 35850

So okay this is another find the volume of the cylinder type of question.

Step 1 Recognise which axis is the region rotated on.
Step 2 Know the volume of the cone and note that the x-axis represents the height using the concept of the cone through the rotation about the x-axis in $y=x$
Step 3 Write in $\pi\int_{0}^{1}y^{2}dx$ because the boundaries are 0 and 1 which is the height thus explaining this part $\int_{0}^{1}$
Step 4 Write in $\pi\int_{0}^{1}x^{2}\left(1-x^{2}\right)^{2}dx$
Step 5 Expand $\left(1-x^{2}\right)^{2}=1-2x^{2}+x^{4}$
Step 6 Multiply by $x^{2}$
Step 7 Integrate $\pi\int_{0}^{1}x^{2}-2x^{4}+x^{6}dx$
Step 8 Solve $\frac{1}{3}-\frac{2}{5}+\frac{1}{7}$ by completing the calculation.

What you will see here @Farhanthestudent005 is that you need to know what the volume of the cylinder is but with a minuscule height because at the end of the day when you rotate a graph along either the x or y-axis or z-axis if you are in 2nd-year uni or above you are inevitably going to have circles and the area of the circle is $\pi{r^{2}}$ so then to find the volume of the cylinder you have to have $\pi{r^{2}}h$ or to recognise the pattern it will be $\pi\int_{lower bound}^{upper bound}\left(x \cup y\right)^{2}d\left(Rotation along the ... axis\right)$

5uckerberg · Jun 22, 2022

If you have any difficulties feel free to reply to the post and someone will help you along your mathematical journey.

Maths Ext help (1 Viewer)

Farhanthestudent005

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cossine

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5uckerberg

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5uckerberg

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