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Fundamental theorem of calculus
Related Topics
Wize University Calculus 2 Textbook > Integration
Fundamental Theorem of Calculus (FTC)
7 Activities
If
∫
0
2
[
3
(
k
x
)
2
+
(
k
+
1
)
x
+
1
]
d
x
=
10
\displaystyle \int_0^2[3(kx)^2+(k+1)x+1]dx=10
∫
0
2
[
3
(
k
x
)
2
+
(
k
+
1
)
x
+
1
]
d
x
=
10
, then what is a possible value of
k
k
k
?
-1
-1/10
0
1/10
1
I don't know
Check Submission
More Fundamental Theorem of Calculus (FTC) Questions:
Fundamental theorem of calculus
Find the derivative
d
d
x
\displaystyle \frac{d}{dx}
d
x
d
of the integral
∫
0
x
2
sin
t
2
d
t
\displaystyle \int_{0}^{x^2}\sin{t^2}\,\text{d}t
∫
0
x
2
sin
t
2
d
t
.
Fundamental theorem of calculus
Find the derivative
d
d
x
\displaystyle \frac{d}{dx}
d
x
d
of the integral
∫
0
x
2
sin
t
2
d
t
\displaystyle \int_{0}^{x^2}\sin{t^2}\,\text{d}t
∫
0
x
2
sin
t
2
d
t
.
Fundamental theorem of calculus
Find the derivative
d
d
x
\displaystyle \frac{d}{dx}
d
x
d
of the integral
∫
0
x
2
sin
t
2
d
t
\displaystyle \int_{0}^{x^2}\sin{t^2}\,\text{d}t
∫
0
x
2
sin
t
2
d
t
.
Application of Fundamental Theorem of Calculus
For what values of
x
x
x
is the function
f
(
x
)
=
∫
x
2
2
(
t
−
1
)
d
t
f\left(x\right)=\int_{x^2}^2\left(t-1\right)dt
f
(
x
)
=
∫
x
2
2
(
t
−
1
)
d
t
decreasing?
Fundamental theorem of calculus
Find the derivative
d
d
x
\displaystyle \frac{d}{dx}
d
x
d
of the integral
∫
0
x
2
sin
t
2
d
t
\displaystyle \int_{0}^{x^2}\sin{t^2}\,\text{d}t
∫
0
x
2
sin
t
2
d
t
.