In each part, make the indicate u -substitution, and then find an integral formula in the Endpaper Integral Table that can be used to evaluate the integral. Do not evaluate the integral. a ∫ x 1 + e x 2 d x ; u = x 2 ______ b ∫ e x d x ; u = x ______ c ∫ e x 1 + sin e x d x ; u = e x ______ d ∫ 1 1 − 4 x 2 3 / 2 d x ; u = 2 x ______
In each part, make the indicate u -substitution, and then find an integral formula in the Endpaper Integral Table that can be used to evaluate the integral. Do not evaluate the integral. a ∫ x 1 + e x 2 d x ; u = x 2 ______ b ∫ e x d x ; u = x ______ c ∫ e x 1 + sin e x d x ; u = e x ______ d ∫ 1 1 − 4 x 2 3 / 2 d x ; u = 2 x ______
In each part, make the indicate u-substitution, and then find an integral formula in the Endpaper Integral Table that can be used to evaluate the integral. Do not evaluate the integral.
a
∫
x
1
+
e
x
2
d
x
;
u
=
x
2
______
b
∫
e
x
d
x
;
u
=
x
______
c
∫
e
x
1
+
sin
e
x
d
x
;
u
=
e
x
______
d
∫
1
1
−
4
x
2
3
/
2
d
x
;
u
=
2
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.
Identify if the integrals are proper or not. If improper, state the rule violated. Identify the u, du, theform of the integral, and the formula to be used. Simplify the function/ equation if necessary.
Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the
corresponding indefinite integral.
Enter the exact answer.
xy1+ xdx =
Evaluate the integral using an appropriate substitution.
NOTE: Enter the exact answer.
-9r
-9x3
d.x
+C
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