If $f(x): Bbb RtoBbb R$ is a continuous function and $f(x)+f(3-x)=4$, find the value of $∫_0^3f(x)dx$
If $f(x): Bbb RtoBbb R$ is a continuous function and $f(x)+f(3-x)=4$, find the value of $∫_0^3f(x)dx$
I couldn't understand how to relate the continuity of the function with the given condition to find the integral.
limits definite-integrals continuity
edited Nov 23 at 6:07
Tianlalu
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
add a comment |
If $f(x): Bbb RtoBbb R$ is a continuous function and $f(x)+f(3-x)=4$, find the value of $∫_0^3f(x)dx$
I couldn't understand how to relate the continuity of the function with the given condition to find the integral.
limits definite-integrals continuity
edited Nov 23 at 6:07
Tianlalu
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
3
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14
add a comment |
If $f(x): Bbb RtoBbb R$ is a continuous function and $f(x)+f(3-x)=4$, find the value of $∫_0^3f(x)dx$
I couldn't understand how to relate the continuity of the function with the given condition to find the integral.
limits definite-integrals continuity
edited Nov 23 at 6:07
Tianlalu
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
If $f(x): Bbb RtoBbb R$ is a continuous function and $f(x)+f(3-x)=4$, find the value of $∫_0^3f(x)dx$
I couldn't understand how to relate the continuity of the function with the given condition to find the integral.
limits definite-integrals continuity
limits definite-integrals continuity
edited Nov 23 at 6:07
Tianlalu
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
edited Nov 23 at 6:07
Tianlalu
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
edited Nov 23 at 6:07
Tianlalu
3,04521038
edited Nov 23 at 6:07
Tianlalu
3,04521038
edited Nov 23 at 6:07
Tianlalu
3,04521038
3,04521038
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
asked Nov 23 at 6:04
Jyothi Krishna Gudi
114
114
3
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14
add a comment |
3
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14
3
3
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14
add a comment |
1 Answer
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$int_0^{3}f(3-x)dx=int_0^{3} f(x) dx$ by the substitution $y =3-x$. Hence we get $int_0^{3} f(x) dx+int_0^{3} f(x) dx=int_0^3 4~dx=12$ or $int_0^{3} f(x) dx=6$.
edited Nov 23 at 6:12
Tianlalu
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
add a comment |
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$int_0^{3}f(3-x)dx=int_0^{3} f(x) dx$ by the substitution $y =3-x$. Hence we get $int_0^{3} f(x) dx+int_0^{3} f(x) dx=int_0^3 4~dx=12$ or $int_0^{3} f(x) dx=6$.
edited Nov 23 at 6:12
Tianlalu
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
add a comment |
$int_0^{3}f(3-x)dx=int_0^{3} f(x) dx$ by the substitution $y =3-x$. Hence we get $int_0^{3} f(x) dx+int_0^{3} f(x) dx=int_0^3 4~dx=12$ or $int_0^{3} f(x) dx=6$.
edited Nov 23 at 6:12
Tianlalu
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
add a comment |
$int_0^{3}f(3-x)dx=int_0^{3} f(x) dx$ by the substitution $y =3-x$. Hence we get $int_0^{3} f(x) dx+int_0^{3} f(x) dx=int_0^3 4~dx=12$ or $int_0^{3} f(x) dx=6$.
edited Nov 23 at 6:12
Tianlalu
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
$int_0^{3}f(3-x)dx=int_0^{3} f(x) dx$ by the substitution $y =3-x$. Hence we get $int_0^{3} f(x) dx+int_0^{3} f(x) dx=int_0^3 4~dx=12$ or $int_0^{3} f(x) dx=6$.
edited Nov 23 at 6:12
Tianlalu
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
edited Nov 23 at 6:12
Tianlalu
3,04521038
edited Nov 23 at 6:12
Tianlalu
3,04521038
edited Nov 23 at 6:12
Tianlalu
3,04521038
3,04521038
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
answered Nov 23 at 6:07
Kavi Rama Murthy
48.9k31854
48.9k31854
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
add a comment |
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
Many thanks to Tianlalu for editing.
– Kavi Rama Murthy
Nov 23 at 6:14
add a comment |
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3
A cheap idea: This question presupposes that if $f(x) + f(3-x) = 4$, then $int_0^3 f$ is always the same value. Since the constant function $f(x) = 2$ is one such function, we have $int_0^3 f = int_0^3 2 dx = 6$.
– JavaMan
Nov 23 at 6:14