Integration question with power of n

In summary, the conversation discusses solving an integral involving tan(x) and its derivative, sec^2x. The integral is rearranged to show a simple integration problem, with the help of the identity tan^2x+1=sec^2x. The final solution involves factoring the numerator and integrating the remaining terms.
  • #1
thoradicus
45
0
http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w11_qp_33.pdf

Homework Statement


no. 10i
cant do ii and iii without doing i first

Homework Equations


tan(x)
d/dx(tan(x))=sec^2x
1+tan^2x=sec^2x

The Attempt at a Solution


Okay, my terms at first would be u^n+2 +u^n. Then, du/dx = sec^2x, so i get du/1+u^2 = dx.

In the end i got (u^n+2 +u^n)/1+u^2. From then on I am stuck. Or did i do something wrong at first?
 
Physics news on Phys.org
  • #2
You know that u=tan[x] so du=sec2[x]dx.

Let's rearrange the integral a little bit to show the following:

∫tann[x](tan2[x]+1)dx

Remember that dx=du/sec2[x]. However, we need to find sec2[x] in terms of u. We use the following identity of sec2[x]=tan2+1 to show now that dx=du/(u2+1)

∫un(u2+1)/(u2+1)=∫un

This now becomes a simple integration problem and you should be able to do the rest.
 
  • #3
oh great! didnt realize the numerator can be factorised like that. Thanks.
 

Related to Integration question with power of n

What is integration with power of n?

Integration with power of n is a mathematical concept that involves finding the integral of a function raised to a power. It is used to solve problems related to area, volume, and other physical quantities.

How do I solve an integration question with power of n?

To solve an integration question with power of n, you can use techniques such as substitution, integration by parts, or trigonometric substitution. It is important to follow the proper steps and rules of integration to arrive at the correct answer.

Are there any special cases when dealing with integration with power of n?

Yes, there are some special cases when dealing with integration with power of n. For example, if the power is negative, you can use the power rule to rewrite the integral. Also, if the power is a fraction, you can use the power rule and substitution to evaluate the integral.

What are some real-life applications of integration with power of n?

Integration with power of n has many real-life applications in science and engineering. It is used to calculate the area under a curve, which is important in fields such as physics, economics, and biology. It is also used to calculate volumes of irregular shapes, such as in fluid mechanics and architecture.

How can I improve my skills in solving integration questions with power of n?

The best way to improve your skills in solving integration questions with power of n is to practice regularly. You can find many practice problems online or in textbooks. It is also helpful to review the different techniques of integration and their applications. Seeking help from a tutor or attending a math workshop can also be beneficial.

Similar threads

Integrals that keep me up at night
Replies
22
Views
2K
Can you handle this integration with limits problem?
Replies
3
Views
1K
Solve the given first order differential equation
Replies
8
Views
1K
Verify Green's Theorem in the given problem
Replies
10
Views
920
How Do You Integrate tan²x sec^4x dx?
Replies
2
Views
2K
Integral of tan^n (x), reduction fromula?
Replies
1
Views
10K
Integral of 1/(a sin^2 x + b sin x cos x + c cos^2 x)
Replies
2
Views
1K
Volume of solid region double integral
Replies
27
Views
2K
Solving the Integral ∫dx/(1-x)
Replies
3
Views
1K
Vector lines, ratio of vector lines
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top