NIMCET 2015 — Mathematics PYQ

Q: How do I solve NIMCET 2015 Mathematics questions?

Practice NIMCET 2015 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

If $\int e^{x}(f(x) - f'(x)) dx = \phi(x)$ , then the value of $\int e^{x}f(x) dx$ is:

Choose the correct answer:

Explanation

Let $I = \int e^x f(x) dx$ .

Using integration by parts on $I$ :

Take $u = f(x)$ and $v = e^x$ .

\int u v dx = u \int v dx - \int \left( u' \int v dx \right) dx

I = f(x) e^x - \int f'(x) e^x dx

\int e^x f'(x) dx = e^x f(x) - I \quad \dots(1)

Now, the given equation is:

\int e^x (f(x) - f'(x)) dx = \phi(x)

\int e^x f(x) dx - \int e^x f'(x) dx = \phi(x)

Substitute $I$ and equation (1) into the expression:

I - (e^x f(x) - I) = \phi(x)

I - e^x f(x) + I = \phi(x)

2I - e^x f(x) = \phi(x)

2I = \phi(x) + e^x f(x)

I = \frac{1}{2} [\phi(x) + e^x f(x)]

Correct Option: (c)