Indefinite Integrals

Easymathematics

The integral ∫sin(x) dx equals

Select the correct option:

cos(x) + C

-cos(x) + C

sin(x) + C

-sin(x) + C

🔒 Solution Hidden from View

Submit your answer to unlock the detailed step-by-step solution.

About This Question

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.

Looking for more practice? Explore all mathematics questions or browse integral calculus questions on RankGuru.

Rank Guru

Indefinite Integrals

Select the correct option:

Solution

🔒 Solution Hidden from View

More indefinite integrals Practice Questions

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

The integral ∫(1/x) dx equals

The integral ∫x² dx equals

The integral ∫eˣ dx equals

About This Question

Solution

Indefinite Integrals

Select the correct option:

Solution

🔒 Solution Hidden from View

More indefinite integrals Practice Questions

Evaluate ∫ex(x1+xlnx​)dx (Assume x>0 and base e for ln).

The integral ∫(1/x) dx equals

The integral ∫x² dx equals

The integral ∫eˣ dx equals

About This Question

Solution

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