Evaluate the line integral $\int _ { C } y d x + x d y$ , where $C$ is the curve $x = t , y = t ^ { 3 } , 1 \leq t \leq 2$ .
A) $15$
B) $18$
C) $21$
D) $24$
E)$27$
F)$30$
G)$33$
H)$36$

Question

Evaluate the line integral $\int _ { C } y d x + x d y$ , where $C$ is the curve $x = t , y = t ^ { 3 } , 1 \leq t \leq 2$ .
A) $15$
B) $18$
C) $21$
D) $24$
E)$27$
F)$30$
G)$33$ 
H)$36$

Quizplus · Accepted Answer

The line integral is evaluated as follows:$$\int_C y dx + x dy = \int_1^2 (t^3) dt + t (3t^2) dt = \int_1^2 (3t^5 + t^3) dt = \left[\frac{3}{6}t^6 + \frac{1}{4}t^4\right]_1^2 = 15$$

Evaluate the Line Integral ∫Cydx+xdy\int _ { C } y d x + x d y∫C​ydx+xdy

Evaluate the Line Integral $\int _ { C } y d x + x d y$