- #1

RadiationX

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Use trig substitution to find [tex]\int_{0}^{5} \frac{dt}{25 + x^2}dt[/tex]

I can solve it to here [tex]\int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{(25 + tan^2\theta)^2}[/tex]

and from this point i can factor the denominator into [tex]{625(1+ \tan^2\theta)}^2[/tex]

which becomes [tex]625\sec^4\theta[/tex]

now i have the integral [tex]\int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{625\sec^4\theta}[/tex]

this now reduces to [tex]\int_{0}^{\frac{\pi}{4}}\frac{cos^2\theta}{25}[/tex]

and at this point i can use a power reducing formula to get rid of the [tex]\cos^2\theta[/tex]

assuming that the last integral is correct and that i use the power reducing formula to reduce [tex]\cos^2\theta[/tex] correctly, what am i doing wrong?

i have a TI-89 graphing calculator, and when i integrat this problem on it i get a different answer than when i do it by hand. where is my mistake?

this post is incorrect look further down for the correction.

i'm really sorry about this.

I can solve it to here [tex]\int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{(25 + tan^2\theta)^2}[/tex]

and from this point i can factor the denominator into [tex]{625(1+ \tan^2\theta)}^2[/tex]

which becomes [tex]625\sec^4\theta[/tex]

now i have the integral [tex]\int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{625\sec^4\theta}[/tex]

this now reduces to [tex]\int_{0}^{\frac{\pi}{4}}\frac{cos^2\theta}{25}[/tex]

and at this point i can use a power reducing formula to get rid of the [tex]\cos^2\theta[/tex]

assuming that the last integral is correct and that i use the power reducing formula to reduce [tex]\cos^2\theta[/tex] correctly, what am i doing wrong?

i have a TI-89 graphing calculator, and when i integrat this problem on it i get a different answer than when i do it by hand. where is my mistake?

this post is incorrect look further down for the correction.

i'm really sorry about this.

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