Solving for the Integral of sin (x^0.5)

Thread starter fonseh
Start date Jun 3, 2017
Tags

Integrate Sin

In summary, the formula for integrating sin(x^0.5) is ∫sin(x^0.5) dx = 2√xsin(x^0.5) + 2cos(x^0.5) + C. To solve an integral with sin(x^0.5), the substitution method can be used. The power rule cannot be used to integrate sin(x^0.5) and there are special cases where the integral may not converge. In real-life applications, integrating sin(x^0.5) is used in physics, engineering, probability and statistics, and calculus-based physics problems.

Jun 3, 2017

fonseh

Homework Statement

Integrate sin (x^0.5)

Homework Equations

The Attempt at a Solution

I let u = sin (x^0.5) , du/dx = cos [(x)^0.5 ] ( 1/ (x)^0.5 ) , how to proceed ? [/B]

Physics news on Phys.org

Jun 3, 2017

fresh_42

Mentor

Insights Author

2023 Award

Have you tried ##u=\sqrt{x}\,##?

Jun 3, 2017

scottdave

Science Advisor

Homework Helper

Insights Author

Gold Member

Have you tried integration by parts?

1. What is the formula for integrating sin(x^0.5)?

The formula for integrating sin(x^0.5) is ∫sin(x^0.5) dx = 2√xsin(x^0.5) + 2cos(x^0.5) + C.

2. How do you solve an integral with sin(x^0.5)?

To solve an integral with sin(x^0.5), you can use the substitution method. Let u = x^0.5 and then use the identity sin^2(x) + cos^2(x) = 1 to rewrite the integral in terms of u. Then, integrate using the formula for sin(u) and substitute back in for x.

3. Can you use the power rule to integrate sin(x^0.5)?

No, the power rule cannot be used to integrate sin(x^0.5) because the exponent is not a constant. Instead, the substitution method or other integration techniques must be used.

4. Are there any special cases when integrating sin(x^0.5)?

Yes, when the limits of integration involve negative numbers or zero, the integral may not converge. Also, when the value of x is close to zero, the integral may require more advanced techniques to solve.

5. How is integrating sin(x^0.5) used in real-life applications?

The integration of sin(x^0.5) is used in physics and engineering to solve problems involving harmonic motion and oscillation. It is also used in calculating the area under curves in probability and statistics. Additionally, it has applications in calculating the work done by a variable force in calculus-based physics problems.