If the area of bounded between the x-axis and the graph of `y=6x-3x^2`
between the ordinates `x=1a n dx=a`
is `19`
units, then `a`
can take the value
`4or-2`
two value are in (2,3) and one
in `(-1,0)`
two value are in (3,4) and one in
`(-2,-1)`
none of these
Text Solution
AI Generated Solution
To solve the problem, we need to find the value of \( a \) such that the area bounded between the x-axis and the graph of \( y = 6x - 3x^2 \) from \( x = 1 \) to \( x = a \) is equal to 19 square units.
### Step-by-Step Solution:
1. **Set up the integral for the area**:
The area \( A \) under the curve from \( x = 1 \) to \( x = a \) is given by the integral:
\[
A = \int_{1}^{a} (6x - 3x^2) \, dx
...
If the area of bounded between the x-axis and the graph of y=6x-3x^2 between the ordinates x=1 and x=a is 19 units, then a can take the value: (A) 4 or -2 (B) one value is in (2, 3) and one in (-1, 0) (C) one value is in (3, 4) and one in (-2,-1) (D) none of these
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