In each part, evaluate the integral ∫ C ( 3 x + 2 y ) d x + ( 2 x − y ) d y along the stated curve. (a) The line segment from (0,0) to (1,1). (b) The parabolic are y = x 2 from (0,0) to (1, 1). (c) The curve y = sin ( π x / 2 ) from (0,0) to (1, 1). (d) The curve x = y 3 from (0,0) to (1, 1).
In each part, evaluate the integral ∫ C ( 3 x + 2 y ) d x + ( 2 x − y ) d y along the stated curve. (a) The line segment from (0,0) to (1,1). (b) The parabolic are y = x 2 from (0,0) to (1, 1). (c) The curve y = sin ( π x / 2 ) from (0,0) to (1, 1). (d) The curve x = y 3 from (0,0) to (1, 1).
In each part, evaluate the integral
∫
C
(
3
x
+
2
y
)
d
x
+
(
2
x
−
y
)
d
y
along the stated curve.
(a) The line segment from (0,0) to (1,1).
(b) The parabolic are
y
=
x
2
from (0,0) to (1, 1).
(c) The curve
y
=
sin
(
π
x
/
2
)
from (0,0) to (1, 1).
(d) The curve
x
=
y
3
from (0,0) to (1, 1).
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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