Question

Let $$int_{0}^{2} f(x) dx = -3, quad int_{0}^{3} f(x) dx = 15, quad int_{0}^{2} g(x) dx = 1, quad int_{2}^{3} g(x) dx = -5,$$ Use these values to evaluate the given definite integrals. a) $int_{0}^{2} (f(x) + g(x)) dx =$ b) $int_{0}^{3} (f(x) - g(x)) dx =$ c) $int_{2}^{3} (3f(x) + 2g(x)) dx =$ d) Find the value $a$ such that $int_{0}^{3} (af(x) + g(x)) dx = 0.$ $a =$

          Let
$$int_{0}^{2} f(x) dx = -3, quad int_{0}^{3} f(x) dx = 15, quad int_{0}^{2} g(x) dx = 1, quad int_{2}^{3} g(x) dx = -5,$$
Use these values to evaluate the given definite integrals.
a) $int_{0}^{2} (f(x) + g(x)) dx =$
b) $int_{0}^{3} (f(x) - g(x)) dx =$
c) $int_{2}^{3} (3f(x) + 2g(x)) dx =$
d) Find the value $a$ such that $int_{0}^{3} (af(x) + g(x)) dx = 0.$
$a =$

Let

int0^2 f(x) dx = -3, quad int0^3 f(x) dx = 15, quad int0^2 g(x) dx = 1, quad int2^3 g(x) dx = -5,

Use these values to evaluate the given definite integrals.
a) int0^2 (f(x) + g(x)) dx =
b) int0^3 (f(x) - g(x)) dx =
c) int2^3 (3f(x) + 2g(x)) dx =
d) Find the value a such that int0^3 (af(x) + g(x)) dx = 0.
a =

Added by -Ngeles G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

08/19/2023

Step 1

a) (f(x) + g(x)) dx = ∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx = (-3) + 1 = -2 b) (f(x) - g(x)) dx = ∫(f(x) - g(x)) dx = ∫f(x) dx - ∫g(x) dx = (-3) - (-5) = 2 (3f(x) + 2g(x)) dx = 3∫f(x) dx + 2∫g(x) dx = 3(-3) + 2(1) = -7 Show more…

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Let $$int_{0}^{2} f(x) dx = -3, quad int_{0}^{3} f(x) dx = 15, quad int_{0}^{2} g(x) dx = 1, quad int_{2}^{3} g(x) dx = -5,$$ Use these values to evaluate the given definite integrals. a) $int_{0}^{2} (f(x) + g(x)) dx =$ b) $int_{0}^{3} (f(x) - g(x)) dx =$ c) $int_{2}^{3} (3f(x) + 2g(x)) dx =$ d) Find the value $a$ such that $int_{0}^{3} (af(x) + g(x)) dx = 0.$ $a =$