Finding a Region In Exercises 7–12, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − π / 4 π / 4 ( sec 2 x − cos x ) d x
Finding a Region In Exercises 7–12, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − π / 4 π / 4 ( sec 2 x − cos x ) d x
Solution Summary: The author illustrates the graph for the function y=mathrmsec2x.
Finding a Region In Exercises 7–12, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral.
∫
−
π
/
4
π
/
4
(
sec
2
x
−
cos
x
)
d
x
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.
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.
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