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Question

Question: If \(\int _ { 1 } ^ { 4 } f ( x ) d x =\)...

If ∫14f(x)dx=\int _ { 1 } ^ { 4 } f ( x ) d x =

A

80

B

20

C

−20- 20

D

37

Answer

37

Explanation

Solution

∫14f(x)dx=∫12(4x+3)dx+∫24(3x+5)dx\int _ { 1 } ^ { 4 } f ( x ) d x = \int _ { 1 } ^ { 2 } ( 4 x + 3 ) d x + \int _ { 2 } ^ { 4 } ( 3 x + 5 ) d x

=∣2x2+3x∣12+∣3x22+5x∣24=37= \left| 2 x ^ { 2 } + 3 x \right| _ { 1 } ^ { 2 } + \left| \frac { 3 x ^ { 2 } } { 2 } + 5 x \right| _ { 2 } ^ { 4 } = 37.