MAT integration question

https://undergroundmathematics.org/calculus-meets-functions/r8396/solution

Solution to part (iii)

How does the integral of

x^4n−2−2x^2n−1+1 =

1/4n−1−1/n+1

the power of x should increase by 1 and it should be divded by the new power so wheres the x term gone

Reply 1

B_9710

18

Original post by Carman3

https://undergroundmathematics.org/calculus-meets-functions/r8396/solution

Solution to part (iii)

How does the integral of

x^4n−2−2x^2n−1+1 =

1/4n−1−1/n+1

the power of x should increase by 1 and it should be divded by the new power so wheres the x term gone

It's a definite integral with limits, 0 and 1.

Reply 2

nerak99

13

Original post by Carman3

https://undergroundmathematics.org/calculus-meets-functions/r8396/solution

Solution to part (iii)

How does the integral of

x^4n−2−2x^2n−1+1 =

1/4n−1−1/n+1

the power of x should increase by 1 and it should be divded by the new power so wheres the x term gone

If I increase the 4n-2 by 1 I get 4n-1. Because the integration is between limits of zero and 1, when the limit is applied, the x^{whatever power} is just 1 leaving the denominator on its own.

Reply 3

Carman3

OP

12

Original post by B_9710

It's a definite integral with limits, 0 and 1.

Original post by nerak99

If I increase the 4n-2 by 1 I get 4n-1. Because the integration is between limits of zero and 1, when the limit is applied, the x^{whatever power} is just 1 leaving the denominator on its own.