Evaluate the integral.
-$$\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t$$
A) $- \frac { 17 } { 2 } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 )$
B) $- \frac { 23 } { 2 } \mathbf { i } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 ) \mathbf { j }$
C) $- \frac { 17 } { 2 } \mathbf { i } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 ) \mathbf { j }$
D) $5 \frac { \sqrt { 2 } - 2 } { 4 } \mathbf { j }$

Question

Quizplus · Accepted Answer

\begin{align*}
\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t &= \int_{1}^{2}(2-7t)\,dt\cdot\mathbf{i}+\int_{1}^{2}5t^{\frac12}\,dt\cdot\mathbf{j}\
&=\bigg[t^2-7\dfrac{t^2}{2}\bigg]_{1}^{2}\cdot\mathbf{i}+\bigg[5\dfrac{t^\frac32}{\frac32}\bigg]_{1}^{2}\cdot\mathbf{j}\
&=\bigg[\dfrac{-3}{2}\bigg]\cdot\mathbf{i}+\bigg[5\bigg(\dfrac{2\sqrt{2}}{3}-\dfrac{2}{3}\bigg)\bigg]\cdot\mathbf{j}\
&=\boxed{-\dfrac{17}{2}}\cdot\mathbf{i}+\boxed{\dfrac{10}{3}(2\sqrt2-1)}\cdot\mathbf{j}
\end{align*}

Evaluate the Integral ∫12((2−7t)i+5tj)dt\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t∫12​((2−7t)i+5t​j)dt

Evaluate the Integral $\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t$