553 views

### Use the substition u = cos(x) to find the indefinite integral of -12sin(x)cos^3(x) dx

We are given the substitution to use, so the first step is to differentiate "u" with respect to x

du/dx = -sin(x)

Now, to replace the "dx" in the original integrand with something in terms of "du", we rearrange the differential:

dx = -1/sin(x) du

We substitute this into the original expression we are integrating; this gives:

S -12sin(x)cos3(x) (-1/sin(x)) du

Let's do some simplifying here; the negative signs cancel, and so does sin(x):

S 12cos3(x) du

Now, simplify again using u=cos(x); this gives:

S 12u3 du

This is a simple C1-level integration; integrating with respect to "u" and adding a constant of integration, we get:

3u4 + c

For our final answer, replace "u" with cos(x):

3cos4x) + c

1 year ago

Answered by Arnab, an A Level Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 417 SUBJECT SPECIALISTS

£20 /hr

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
-Personal Statements-

“Undergraduate Physicist with lots of experience in teaching in different fields and age groups, looking to instil a passion for learning into students.”

£22 /hr

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

£20 /hr

Degree: Mathematics (Bachelors) - Bath University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I’m Sachin and I study Maths at the University of Bath. I’m looking forward to working with my students to enable them to reach their highest potential.”

Currently unavailable: for new students

Degree: Physics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
History
Computing

“About Me:  I am currently studying Physics at Durham University. I have always loved physics and maths, and I think that anyone can be successful at them if they are taught properly. I believe that if you learn maths and science well,...”

### You may also like...

#### Posts by Arnab

A ball of mass 0.25 kg is travelling with a velocity of 1.2 m/s when it collides with an identical, stationary ball. After the collision, the two balls move together with the same velocity. How fast are they moving?

Use the substition u = cos(x) to find the indefinite integral of -12sin(x)cos^3(x) dx

#### Other A Level Maths questions

Find the value of 2∫1 (6x+1) / (6x2-7x+2) dx, expressing your answer in the form mln(2) + nln(3), where m and n are integers.

What is an integral?

Differentiate y=(x^2+1)(e^-x)

What's the point of writing my mathematics well if I don't get extra marks for it?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.