logo88
Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

ex 3.6
6. find the area enclosed between the curve y= -2x²-5x+3 and the x-axis

Sagot :

When y=0,

[tex]-2{ x }^{ 2 }-5x+3=0\\ \\ 2{ x }^{ 2 }+5x-3=0\\ \\ \left( 2x-1 \right) \left( x+3 \right) =0[/tex]

[tex]\\ \\ \therefore \quad x=\frac { 1 }{ 2 } \\ \\ \therefore \quad x=-3[/tex]

--------------------

[tex]\int _{ -3 }^{ \frac { 1 }{ 2 } }{ -2{ x }^{ 2 } } -5x+3dx[/tex]

[tex]\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }[/tex]

[tex]\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }[/tex]

[tex]\\ \\ \\ =\left\{ -\frac { 2 }{ 3 } { \left( \frac { 1 }{ 2 } \right) }^{ 3 }-\frac { 5 }{ 2 } { \left( \frac { 1 }{ 2 } \right) }^{ 2 }+3\left( \frac { 1 }{ 2 } \right) \right\} -\left\{ -\frac { 2 }{ 3 } { \left( -3 \right) }^{ 3 }-\frac { 5 }{ 2 } { \left( -3 \right) }^{ 2 }+3\left( -3 \right) \right\}[/tex]

[tex]\\ \\ \\ =-\frac { 2 }{ 3 } \cdot \frac { 1 }{ 8 } -\frac { 5 }{ 2 } \cdot \frac { 1 }{ 4 } +\frac { 3 }{ 2 } -\left\{ -\frac { 2 }{ 3 } \left( -27 \right) -\frac { 5 }{ 2 } \cdot 9-9 \right\}[/tex]

[tex]\\ \\ =-\frac { 2 }{ 24 } -\frac { 5 }{ 8 } +\frac { 3 }{ 2 } -\left\{ \frac { 54 }{ 3 } -\frac { 45 }{ 2 } -9 \right\}[/tex]

[tex]\\ \\ =-\frac { 2 }{ 24 } -\frac { 15 }{ 24 } +\frac { 36 }{ 24 } -\frac { 54 }{ 3 } +\frac { 45 }{ 2 } +9[/tex]

[tex]\\ \\ =\frac { 19 }{ 24 } -\frac { 54 }{ 3 } +\frac { 45 }{ 2 } +\frac { 18 }{ 2 } \\ \\ =\frac { 19 }{ 24 } -\frac { 54 }{ 3 } +\frac { 63 }{ 2 }[/tex]

[tex]\\ \\ =\frac { 343 }{ 24 } [/tex]

Answer: 343/24 units squared.
Panoyin
y = -2x² - 5x + 3
-2x² - 5x + 3 = 0
x = -(-5) +/- √(-5² - 4(-2)(3))
                     2(-2)
x = 5 +/- √(25 + 24)
                -4
x = 5 +/- √39
           -4
x = 5 +/- 6.244997998398398
                      -4
x = 5 + 6.244997998398398   x = 5 - 6.244997998398398                     
                       -4                                             -4
x = 11.624997998398398       x = -1.244997998398398
                    -4                                             -4
x = -2.8112494995996           x = 0.3112494995996
-----------------------------------------------------------------------------------------------
y = -2x² - 5x + 3                      y = -2x² - 5x + 3
y = -2(-3)² - 5(-3) + 3               y = -2(0.3)² - 5(0.3) + 3
y = -2(9) + 15 + 3                    y = -2(0.09) - 0.15 + 3
y = -18 + 15 + 3                      y = -0.18 - 0.15 + 3
y = -3 + 3                                y = -0.33 + 3
y = 0                                       y = 2.67
-----------------------------------------------------------------------------------------------
(x, y) = (-3, 0)                          (x, y) = (0.3, 2.67)
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.