## Calculus 8th Edition

$2\mathbf{\hat{i}}-4\mathbf{\hat{j}}+32\mathbf{\hat{k}}$
1) Anti-differentiate and evaluate $\int_{0}^{2} (t\mathbf{\hat{i}}- t^3\mathbf{\hat{j}}+ 3t^5\mathbf{\hat{k}})dt$ using power rule. $$\left[\frac{1}{2}t^2\mathbf{\hat{i}}- \frac{1}{4}t^4\mathbf{\hat{j}}+ \frac{1}{2}t^6\mathbf{\hat{k}}\right]_{0}^{2}\\ =\left[\frac{1}{2}(2)^2\mathbf{\hat{i}}- \frac{1}{4}(2)^4\mathbf{\hat{j}}+ \frac{1}{2}(2)^6\mathbf{\hat{k}}\right]- \left[\frac{1}{2}(0)^2\mathbf{\hat{i}}- \frac{1}{4}(0)^4\mathbf{\hat{j}}+ \frac{1}{2}(0)^6\mathbf{\hat{k}}\right]\\ =2\mathbf{\hat{i}}-4\mathbf{\hat{j}}+32\mathbf{\hat{k}}$$