Solve Definite Integral: π/2 to 0

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Homework Help Overview

The discussion revolves around solving definite integrals, specifically one from 0 to π/2 and another involving sin(x) and e^(x^2). Participants are exploring methods to approach these integrals within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing potential methods for solving the integrals, including substitution and integration by parts. There is uncertainty about the effectiveness of these methods for the given problems.

Discussion Status

Some participants have offered suggestions for methods, such as integration by parts for one of the integrals. There is ongoing exploration of whether the integrand in the second integral is an even function, which may influence the approach.

Contextual Notes

Participants are grappling with the choice of techniques for integration and the implications of the properties of the functions involved. There is a noted lack of consensus on the best approach to take for the second integral.

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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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What exactly are you asking?
 
what to use to solve them - especially the second one- I've tried substitution but got me nowhere
 
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.
 
thanks :)
 
For the second one:

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

[tex]\int x\cos(x) dx[/tex]
 

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