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Integrals: Geometric Definitions
Related Topics
Wize University Calculus 1 Textbook > Integrals
Computing Definite Integrals Geometrically
3 Activities
Evaluate the definite integral
∫
5
−
6
5
+
6
−
x
2
+
10
x
−
19
d
x
\displaystyle\int_{5-\sqrt{6}}^{5+\sqrt{6}}\sqrt{-x^2+10x-19}\de{x}
∫
5
−
6
5
+
6
−
x
2
+
10
x
−
19
d
x
.
Answer
I don't know
Check Submission
More Computing Definite Integrals Geometrically Questions:
Practice: Circle
Q:
\textbf{Q:}
Q:
Find
∫
2
4
4
−
(
x
−
2
)
2
\displaystyle\int_2^4\sqrt{4-\left(x-2\right)^2}
∫
2
4
4
−
(
x
−
2
)
2
Definite Integrals
Calculate
∫
0
1
∣
x
−
1
∣
d
x
\int_0^1|x-1|dx
∫
0
1
∣
x
−
1∣
d
x
(Hint: Sketch a Graph)
Practice: Circle
Q:
\textbf{Q:}
Q:
Find
∫
2
4
4
−
(
x
−
2
)
2
\displaystyle\int_2^4\sqrt{4-\left(x-2\right)^2}
∫
2
4
4
−
(
x
−
2
)
2
Evaluate
∫
−
1
1
1
−
x
2
d
x
\int_{-1}^1\sqrt{1-x^2}dx
∫
−
1
1
1
−
x
2
d
x
.
Hint:
x
2
+
y
2
=
r
2
x^2+y^2=r^2
x
2
+
y
2
=
r
2
is a circle of radius r centered at
(
0
,
0
)
(0,0)
(
0
,
0
)
. Try to draw the curve in this integral.
Integrating Even and Odd Functions: Definite Integrals
Evaluate
∫
−
1
1
4
−
(
x
+
1
)
2
+
sin
x
⋅
e
2
x
4
d
x
\int_{-1}^1\sqrt{4-\left(x+1\right)^2}+\sin x\cdot e^{2x^4}\ dx
∫
−
1
1
4
−
(
x
+
1
)
2
+
sin
x
⋅
e
2
x
4
d
x
.