Let \mathbf{f}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}. Calculate the following:
(a) \int \mathbf{f}(t) d t. (b) \int_{0}^{\pi / 2} \mathbf{f}(t) d t.
Let \mathbf{f}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}. Calculate the following:
(a) \int \mathbf{f}(t) d t. (b) \int_{0}^{\pi / 2} \mathbf{f}(t) d t.