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Suppose that f is continuous, [tex]\int\limits^5__-2 \,[/tex] f(x)dx=11 and [tex]\int\limits^2__-2 \,[/tex] f(x)dx=14 . Find the value of the integral [tex]\int\limits^2_5 \,[/tex] f(x)dx.

Suppose that f is continuous texintlimits52 tex fxdx11 and texintlimits22 tex fxdx14 Find the value of the integral texintlimits25 tex fxdx class=

Respuesta :

Answer:

3

Step-by-step explanation:

[tex]\int_{-2}^{5} f(x)dx=11[/tex] implies [tex]\int_5^{-2}f(x)dx=-11[/tex]

[tex]\int_5^2f(x)dx=\int_c^2f(x)dx+\int_5^cf(x)dx[/tex]

where in this case we will let [tex]c=-2[/tex] for our purposes.

[tex]\int_5^{2}f(x)dx=\int_{-2}^2f(x)dx+\int_5^{-2}f(x)dx[/tex]

[tex]\int_5^2f(x)dx=14+(-11)[/tex]

[tex]\int_5^{2}f(x)dx=3[/tex]

amna04352

Answer:

3

Step-by-step explanation:

[-2, 5] = [-2, 2] + [2, 5]

11 = 14 + [2, 5]

[2, 5] = 11 - 14 = -3

[5, 2] = -(-3) = 3

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