I'm just running through my maths book and have got stuck on solving this problem. Being... find the value of:
∫[1,0] 1/√(9-4t²) dt
Try as I might I just cannot work out the correct way to integrate this. I've been trying to use this conversion method:
f'(x) = 1/√(a²-t²) ≈ f(x) = sin-¹(t/a)+c
But I don't get the right answer according to the book no matter what I do. The book says that the value should be 0.365, but I just don't seem to hit the jackpot no matter how I arrange it. I'm assuming it has something to do with the co-efficient of 4 but hey, who knows. Hopefully one of you do and can explain where I'm going wrong..
Cheers in advance