The integral you're asking about seems to be:

\[
\int 4\sin(x) \, dx
\]

This is a straightforward integral. Here's how we solve it:

\[
\int 4\sin(x) \, dx = 4 \int \sin(x) \, dx
\]

The integral of \(\sin(x)\) is \(-\cos(x)\), so:

\[
4 \int \sin(x) \, dx = 4(-\cos(x)) = -4\cos(x) + C
\]

where \(C\) is the constant of integration.

The final answer is:

\[
-4\cos(x) + C
\]

Would you like further details, or have any other questions?

Here are five related questions for practice:
1. What is \(\int \cos(x) \, dx\)?
2. Can you solve \(\int 4\cos(x) \, dx\)?
3. What is \(\int \sin^2(x) \, dx\)?
4. How do you compute \(\int e^x \sin(x) \, dx\)?
5. Solve \(\int \sin(ax) \, dx\), where \(a\) is a constant.

**Tip**: Always factor constants out of the integral to simplify the expression before integrating.

Discover how to solve the integral of 4sin(x) dx with a comprehensive step-by-step explanation. This problem explores key concepts in calculus and trigonometry, using the integral of the sine function formula. Ideal for students in Grades 11-12 or those in early college-level calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation