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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET - Mathematics - Calculus - Integration

231. The integral of \( \int x^n \, dx \), where \( n \neq -1 \), is:
A) \( \frac{x^{n+1}}{n+1} + C \)
B) \( \frac{x^{n+1}}{n-1} + C \)
C) \( \frac{x^{n}}{n} + C \)
D) \( \frac{x^{n+1}}{n+2} + C \)

Answer: A) \( \frac{x^{n+1}}{n+1} + C \)

232. The integral of \( \int e^x \, dx \) is:
A) \( e^x + C \)
B) \( e^{-x} + C \)
C) \( \frac{e^x}{x} + C \)
D) \( x e^x + C \)

Answer: A) \( e^x + C \)

233. The integral of \( \int \ln x \, dx \) is:
A) \( x \ln x - x + C \)
B) \( x \ln x + x + C \)
C) \( \frac{x}{\ln x} + C \)
D) \( \ln x + C \)

Answer: A) \( x \ln x - x + C \)

234. The formula for integration by parts is:
A) \( \int u \, dv = uv - \int v \, du \)
B) \( \int u \, dv = uv + \int v \, du \)
C) \( \int u \, dv = u^2 - v^2 \)
D) \( \int u \, dv = u + v \)

Answer: A) \( \int u \, dv = uv - \int v \, du \)

235. The integral of \( \int \sin x \, dx \) is:
A) \( -\cos x + C \)
B) \( \cos x + C \)
C) \( -\sin x + C \)
D) \( \sin x + C \)

Answer: A) \( -\cos x + C \)

236. The integral of \( \int \frac{1}{x} \, dx \) is:
A) \( \ln |x| + C \)
B) \( x \ln |x| + C \)
C) \( \frac{1}{x} + C \)
D) \( \ln x + C \)

Answer: A) \( \ln |x| + C \)

237. The method of partial fractions is used to integrate functions of the form:
A) \( \frac{1}{(x-a)(x-b)} \)
B) \( \frac{1}{x^2 + 1} \)
C) \( \frac{e^x}{x} \)
D) \( \frac{1}{x} \)

Answer: A) \( \frac{1}{(x-a)(x-b)} \)

238. The integral of \( \int \cos x \, dx \) is:
A) \( \sin x + C \)
B) \( -\sin x + C \)
C) \( \cos x + C \)
D) \( -\cos x + C \)

Answer: A) \( \sin x + C \)

239. Which of the following is the integral of \( \int \frac{dx}{x^2 + a^2} \)?
A) \( \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C \)
B) \( \frac{x}{a^2 + x^2} + C \)
C) \( \ln |x| + C \)
D) \( \frac{x}{a} + C \)

Answer: A) \( \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C \)

240. The reduction formula for \( \int \sin^n x \, dx \) is given by:
A) \( \int \sin^n x \, dx = \frac{-\cos x \sin^{n-1} x}{n} + C \)
B) \( \int \sin^n x \, dx = \frac{n-1}{n} \cos x + C \)
C) \( \int \sin^n x \, dx = \frac{1}{n} \sin^{n+1} x + C \)
D) \( \int \sin^n x \, dx = \frac{1}{n+1} \sin^{n+1} x + C \)

Answer: A) \( \int \sin^n x \, dx = \frac{-\cos x \sin^{n-1} x}{n} + C \)

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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET - Mathematics - Calculus - Integration

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