Indefinite Integrals

Easymathematics

The integral ∫sin(x) dx equals

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cos(x) + C

-cos(x) + C

sin(x) + C

-sin(x) + C

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Subject: mathematics
Chapter: integral calculus
Topic: indefinite integrals
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

-cos(x) + C

Standard Integral: The integral of a trigonometric function is the reverse process of differentiation.
Reasoning: Since $\frac{d}{d x} (cos x) = - sin x$ , it follows that $\frac{d}{d x} (- cos x) = sin x$ .
Result: Therefore, $\int sin x d x = - cos x + C$ .
Caution: Students often confuse this with the derivative of $sin x$ (which is $+ cos x$ ). Reminder: Integration of $sin$ is negative $cos$ .

This easy difficulty mathematics question is from the chapter integral calculus, covering the topic of indefinite integrals. It appeared in the 2025 exam.

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Indefinite Integrals

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Indefinite Integrals

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Solution

Evaluate $\int e^{x} (\frac{1 + x l n x}{x}) d x$ (Assume $x > 0$ and base $e$ for $ln$ ).