(A) Find $g ( t )$ So That $\int g ( t ) d t = \frac { t } { 2 } \sqrt { 4 - t ^ { 2 } } + 2 \cdot \sin ^ { - 1 } \frac { t } { 2 }$

Essay

(a) Find $g ( t )$ so that $\int g ( t ) d t = \frac { t } { 2 } \sqrt { 4 - t ^ { 2 } } + 2 \cdot \sin ^ { - 1 } \frac { t } { 2 }$ (b) Evaluate $\int _ { 0 } ^ { 2 } g ( t ) d t$ using the Evaluation Theorem.(c) Evaluate $\int _ { 0 } ^ { 2 } g ( t ) d t$ by the area interpretation of the integral. Compare your answer with part (b) above.(d) Evaluate $\int _ { 0 } ^ { \sqrt { 3 } } g ( t ) d t .$