UrbanPro
true

Take Engineering Diploma Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Search in

Integration by substitution.

B.Sudhakar
03/01/2017 0 0

Let's solve an example using 'u' substitution method.

∫ sin² x cos x dx ------------------------A

As we can see " cos x " along with " sin x " and we don't have any ready made formula for the product of two functions in integration, let's try to eliminate one of them. As cos x is raised to power one, we can eliminate cos x by using ' u ' substitution.

Let u = sin x,   by differentiating  "u " wrt "x "  du / dx = cos x or  dx = du / cos x

By substituting "u" and "dx" in  "A"

∫ sin² x cos x dx = ∫ u² cos x du / cos x

= ∫ u² cos x / cos x du.               ( cos x cancels out )

∫ u² du

= u³ / 3 + c  

=1/3 sin³ x + c.    (by substituting "sin x" back in place of " u ")

∴ ∫ sin² x cos x dx = 1/3 sin³ x + c

 

 

0 Dislike
Follow 0

Please Enter a comment

Submit

Other Lessons for You

Intro to C Programming
C is one of the most popular computer language today. C language was developed by Dennis Ritchie in 1972. C is portable, Robust, Procedure oriented, High level programming language. C requires compiler...

Wheeled Robots
For safety, speed and fuel efficiency, when designing recreation and transportation vehicles, engineers take into account all forces acting on the object. Engineers consider drag forces when they design...

Metrical Constructions And Engineering Curves
• Divide a line into any number of equal parts by parallel line method bisecting of line and angle. • Construction of triangles and polygons Introduction of conic sections...

Capacitor Construction
• A capacitor is constructed using a pair of parallel conducting plates separated by an insulating material (dielectric). • When the two plates of a capacitor are connected to a voltage source...

Lazy initialization Vs Eager initialization
Memory and resource utilization plays crucial role in current enterprise era developers always need to take care of resource creation, utilization and it's cleanness on correct time to make application...
M
X

Looking for Engineering Diploma Tuition Classes?

The best tutors for Engineering Diploma Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Engineering Diploma Tuition with the Best Tutors

The best Tutors for Engineering Diploma Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more