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.
The equation of the tangent to the curve y = x' – 3x – 2x + 2 at the point where the curve cuts the y-
axis is
Select one:
O y = x - 1
O y = -2x + 4
O y = x + 2
O y = 2x + 2
O y = -2x + 2
Find the points on the graph of z = xy' + 8y¯' where the tangent plane is parallel to 9x + 5y + 9z = 0.
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(Give your answer as a comma-separated list of points in the form (*, *, *). Express numbers in exact form. Use symbolic
notation and fractions where needed.)
point(s):
1 of 17 >
Find the equation of the tangent plane to the graph of
f(x, y) = In (14x² – 11y²)
at the point (1, 1).
(Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.)
the equation:
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