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.
j)
f) lim
x+x ex
g) lim Inx
h) lim x-5
i) lim arctan x
x700
lim arctanx
811x
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
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