Solve Definite Integral: π/2 to 0

In summary, to solve the given integrals, use integration by parts for the first one and substitution or integration by parts for the second one.
  • #1
s883
5
0

Homework Statement


π/2
d x/
(x2 - 2x cosx + 1)
0


п
sin x. ex^2dx
-п


Homework Equations





The Attempt at a Solution






 
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  • #2
What exactly are you asking?
 
  • #3
what to use to solve them - especially the second one- I've tried substitution but got me nowhere
 
  • #4
For the second one, try integration by parts. Not sure myself if it will work, but by looking at it I see two functions multiplied together. Anything like that you should think substitution or interation by parts.
 
  • #5
thanks :)
 
  • #6
For the second one:

Isn't the integrand an even function?
 
  • #7
For the first one, use integration by parts for:

[tex]\int x\cos(x) dx[/tex]
 

1. What is a definite integral?

A definite integral is a mathematical concept that represents the area under a curve between two points on the x-axis. It is used to calculate the total change of a function over a specific interval.

2. How do you solve a definite integral?

To solve a definite integral, you need to first evaluate the integral by finding the antiderivative of the function, then plug in the upper and lower limits of integration and subtract the results. This will give you the numerical value of the integral.

3. Why is the upper limit of integration always listed first in a definite integral?

The upper limit of integration is listed first in a definite integral because it represents the end point of the interval. This follows the convention of reading from left to right and makes the integral easier to understand and evaluate.

4. Can you use the definite integral to find the area under a curve?

Yes, the definite integral is specifically designed to find the area under a curve. By evaluating the definite integral between two points on the x-axis, you can calculate the area of the region between the curve and the x-axis.

5. What does it mean when the limits of integration are π/2 and 0?

The limits of integration represent the starting and ending points of the interval over which you are calculating the definite integral. In this case, the interval is from π/2 to 0, meaning you are finding the area under the curve between the points π/2 and 0 on the x-axis.

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