Let the equation of a curve passing through point be given by . If the equation of curve is written in the form , then is

None of these Explanation: Step 1: Evaluate the Integral The given equation is: We can use the substitution method . Let: Then, the derivative is: Substitute these into the integral: Substituting back : Step 2: Find the Constant The curve passes through the point . This means when , . So, the equation of the curve is: Step 3: Express in terms of To find , we need to isolate : Multiply the entire equation by : Subtract from both sides: Take the natural logarithm ( ) of both sides: Take the cube root: Final Answer: The function is:

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JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

Let the equation of a curve passing through point $(0, 1)$ be given by $y = \int x^{2} e^{x^{3}} d x$ . If the equation of curve is written in the form $x = f (y)$ , then $f (y)$ is

JAMIA 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

Step 1: Evaluate the Integral

Step 2: Find the Constant $C$

Step 3: Express $x$ in terms of $y$

Explanation

Step 1: Evaluate the Integral

Step 2: Find the Constant $C$

Step 3: Express $x$ in terms of $y$

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