Finding and Checking an Integral In Exercises 67-74, (a) integrate to find F as a function of x , and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F ( x ) = ∫ π / 3 x sec t tan t d t
Finding and Checking an Integral In Exercises 67-74, (a) integrate to find F as a function of x , and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F ( x ) = ∫ π / 3 x sec t tan t d t
Solution Summary: The author explains how the function is integrated within the limits of cF(x)=displaystyle
Finding and Checking an Integral In Exercises 67-74, (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a).
F
(
x
)
=
∫
π
/
3
x
sec
t
tan
t
d
t
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Curve sketching for the function
f(x) =
x-ex
X
a) What is the domain of f(x).
b) Is the function odd, even or neither odd nor even?
c) What are the zeros of f(x)?
d) What are the poles of f(x)?
e) Calculate the first three derivatives of f(x).
f) Determine the turning points of f(x).
g) Determine the inflection points of f(x).
h) What is the limit of f(x) for x → ±∞o?
Finding an Indefinite Integral In Exercises
9–30, find the indefinite integral and check the
result by differentiation.
x(5x2 + 4)° dx
15.
16.
x?
;dx
(1 + x³)?
6x?
23.
24.
dx
(4x3 – 9)3
-
Think About It Because f(t) = sin t is an oddfunction and g(t) = cos t is an even function, what canbe said about the function h(t) = f(t)g(t)?
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