Line integral and Green's theorem

Exercise4.1
1. Find the following line integrals.
(a)
$\int_{c}y dx,  C: y = 1 -x,  0 \leq x \leq 1$
(b)
$\int_{c}x^2 dy,  C: y = 1 -x,  0 \leq x \leq 1$
(c)
$\int_{c}(xy dx - y^2 dy),  C: y = x^2,  -1 \leq x \leq 1$
(d)
$\int_{c}(xy dx - x^3 dy),  C: x = \cos{\theta}, y = \sin{\theta},  0 \leq \theta \leq 2\pi$

2. Find the following line integral for the parameter $t$

(a)
$\int_{c}(x^2 + y)dt,  C: x = \sqrt{t}, y = 1 - t^2,  0 \leq t \leq 1$
(b)
$\int_{c}xy^2 dt,  C: x = \sin{t}, y = \sin^{2}{t},  0 \leq t \leq \frac{\pi}{2}$

3. Using Green's theorem, evaluate the following line integral.

(a)
$\int_{c}(x^2 y dx - xy^2 dy),  C:$   unit circle
(b)
$\int_{c}(y dx + 2x dy),  C:$   first quadrand quater circle