0
votes
1answer
107 views

IB Math question: Fresnel integral?

P moves along x-axis such that its velocity, v, at time t is given by $v=\cos(t^2)$. Find the time at which the total distance travelled by P is 1. (all in meters, meters/sec). So the total distance ...
0
votes
2answers
73 views

Evaluating $\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$

$$\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$$ How to solve this trigonometric integral? I can't find any solutions. Some books suggest to use Fresnel integral. I would be grateful if you could ...
11
votes
1answer
196 views

Need help with $\int_0^\infty\left(\pi\,x+\frac{S(x)\cos\frac{\pi x^2}2-C(x)\sin\frac{\pi x^2}2}{S(x)^2+C(x)^2}\right)dx$

Let $$I=\int_0^\infty\left(\pi\,x+\frac{S(x)\cos\frac{\pi x^2}2-C(x)\sin\frac{\pi x^2}2}{S(x)^2+C(x)^2}\right)dx,\tag1$$ where $$S(x)=-\frac12+\int_0^x\sin\frac{\pi t^2}2dt,\tag2$$ ...
5
votes
1answer
148 views

Definite integral involving Fresnel integrals

I am seeking to evaluate $\int_0^{\infty} f(x)/x^2 \, dx$ with $f(x)=1-\sqrt{\pi/6} \left(\cos (x) C\left(\sqrt{\frac{6 x}{\pi }} \right)+S\left(\sqrt{\frac{6 x}{\pi }} \right) \sin ...