CUET PG 2022 — Mathematics PYQ

The given curve is:

Taking the cube root of both sides, we get:

Step 2: Set up the Definite Integral

The area $A$ enclosed between a curve $x=f(y)$ and the lines $y=c$ and $y=d$ is given by:

Given the boundaries $y=1$ and $y=8$:

Step 3: Evaluate the Integral

Using the power rule for integration $\int y^{n}dy=\frac{y^{n+1}}{n+1}$:

Now, apply the limits from $1$ to $8$:

Step 4: Simplify the Calculation

• Calculate $8^{4/3}$: $(8^{1/3}{)}^4=(2{)}^4=16$

• Calculate $1^{4/3}$: $1$

Substitute these values back into the equation:

Final Answer:

The area enclosed is $\frac{45}{4}$ or $11.25$ square units.