1. Evaluate \int_b^a (x+3) dx if 0<a<b 2. If \int_0^5 f(x) = 4 , find \int_0^5 [f(x)+2] dx
A anwaname New member Joined Nov 28, 2007 Messages 2 Dec 6, 2007 #1 1. Evaluate \int_b^a (x+3) dx if 0<a<b 2. If \int_0^5 f(x) = 4 , find \int_0^5 [f(x)+2] dx
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Dec 6, 2007 #2 Hello, anwaname! Here's the second one . . . 2. If ∫05 f(x) = 4, find: ∫05[f(x)+2] dx\displaystyle \text{2. If }\int_0^5\!\! f(x) \:= \:4\text{, find: }\:\int_0^5 [f(x)+2]\,dx2. If ∫05f(x)=4, find: ∫05[f(x)+2]dx Click to expand... We have: ∫05 f(x) dx⏟+∫05 2 dx⏟\displaystyle \text{We have: }\;\underbrace{\int^5_0\!\! f(x)\,dx} + \underbrace{\int^5_0\!\! 2\,dx}We have: ∫05f(x)dx+∫052dx . . . . . . . . . . =4+2x ∣05\displaystyle = \quad4 \qquad +\quad 2x\,\bigg|^5_0=4+2x∣∣∣∣∣05 . . . . . . . . . . =4+(10−0)\displaystyle =\quad 4 \quad+\quad(10 - 0)=4+(10−0) . . . . . . . . . . =14\displaystyle =\qquad 14=14
Hello, anwaname! Here's the second one . . . 2. If ∫05 f(x) = 4, find: ∫05[f(x)+2] dx\displaystyle \text{2. If }\int_0^5\!\! f(x) \:= \:4\text{, find: }\:\int_0^5 [f(x)+2]\,dx2. If ∫05f(x)=4, find: ∫05[f(x)+2]dx Click to expand... We have: ∫05 f(x) dx⏟+∫05 2 dx⏟\displaystyle \text{We have: }\;\underbrace{\int^5_0\!\! f(x)\,dx} + \underbrace{\int^5_0\!\! 2\,dx}We have: ∫05f(x)dx+∫052dx . . . . . . . . . . =4+2x ∣05\displaystyle = \quad4 \qquad +\quad 2x\,\bigg|^5_0=4+2x∣∣∣∣∣05 . . . . . . . . . . =4+(10−0)\displaystyle =\quad 4 \quad+\quad(10 - 0)=4+(10−0) . . . . . . . . . . =14\displaystyle =\qquad 14=14
D Deleted member 4993 Guest Dec 6, 2007 #3 anwaname said: 1. Evaluate \int_b^a (x+3) dx if 0<a<b 2. If \int_0^5 f(x) = 4 , find \int_0^5 [f(x)+2] dx Click to expand... The problem #1 is straight-forward. Please show us your work and exactly where you are stuck - so that we know where to begin to help you.
anwaname said: 1. Evaluate \int_b^a (x+3) dx if 0<a<b 2. If \int_0^5 f(x) = 4 , find \int_0^5 [f(x)+2] dx Click to expand... The problem #1 is straight-forward. Please show us your work and exactly where you are stuck - so that we know where to begin to help you.
