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If and are two antiderivatives of such that then find the area of the triangle formed…
MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals
Problem
If
f
1
(
x
)
f_1(x)
f
1
(
x
)
and
f
2
(
x
)
f_2(x)
f
2
(
x
)
are two antiderivatives of
f
(
x
)
=
a
x
+
b
+
sin
(
x
)
f(x) = ax + b + \sin(x)
f
(
x
)
=
a
x
+
b
+
sin
(
x
)
such that
∫
2
4
(
f
1
(
x
)
−
f
2
(
x
)
)
d
x
=
8
\int_2^4 (f_1(x) - f_2(x))\,dx = 8
∫
2
4
(
f
1
(
x
)
−
f
2
(
x
))
d
x
=
8
then find the area of the triangle formed by joining the points
(
3
,
f
1
(
3
)
)
,
(
3
,
f
2
(
3
)
)
(3, f_1(3)), (3, f_2(3))
(
3
,
f
1
(
3
))
,
(
3
,
f
2
(
3
))
and the origin.
Related theory
Antiderivatives
Standard algebraic integrals
Integration as inverse process of differentiation
Integrals
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