Evaluate the definite integrals using properties of the definite integral and the fact thatf(x) dx-5f (x) dæ = 8, andg(x) dz = 4.=-3,(a)10f (x) adx =Number(b)f (x) da =Number(c)| ( (z) – 9 (2)) dNumber(d)(2f (x) + 3g (x)) da = Number

given : ∫-52f(x)dx=-3 , ∫24f(x)dx=8 , ∫24g(x)dx=8(a) ∫-5210f(x)dx=10∫-52f(x)dx=10×(-3)=-30…

Evaluate the definite integrals using properties of the definite integral and the fact that 4. 4 Lfe) da - -3.f(2) da = 8, and f (x) dr 8, and g(x) dx = 4. (a) 10f (x) dæ = Number (b) f (x) da Number (c) (f (x) – 9 (x)) dx = Number (d) | (2f (z) + 39 (x)) dæ = Number

Evaluate the definite integrals using properties of the definite integral and the fact that 4. 4 Lfe) da - -3.f(2) da = 8, and f (x) dr 8, and g(x) dx = 4. (a) 10f (x) dæ = Number (b) f (x) da Number (c) (f (x) – 9 (x)) dx = Number (d) | (2f (z) + 39 (x)) dæ = Number

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.3: Area And The Definite Integral

Problem 1E: Explain the difference between an indefinite integral and a definite integral.

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Question

Evaluate the definite integrals using properties of the definite integral and the fact that
f(x) dx
-5
f (x) dæ = 8, and
g(x) dz = 4.
=-3,
(a)
10f (x) a
dx =
Number
(b)
f (x) da =
Number
(c)
| ( (z) – 9 (2)) d
Number
(d)
(2f (x) + 3g (x)) da = Number

Expert Solution

Step 1

$g i v e n : \int_{- 5}^{2} f (x) d x = - 3, \int_{2}^{4} f (x) d x = 8, \int_{2}^{4} g (x) d x = 8 (a) \int_{- 5}^{2} 10 f (x) d x = 10 \int_{- 5}^{2} f (x) d x = 10 \times (- 3) = - 30 \int_{- 5}^{2} 10 f (x) d x = - 30 (b) \int_{- 5}^{4} f (x) d x = \int_{- 5}^{2} f (x) d x + \int_{2}^{4} f (x) d x = - 3 + 8 = 5 \int_{- 5}^{4} f (x) d x = 5$

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