Given curves:
\( y = x^2 - 5x \quad \text{and} \quad y = 7x - x^2 \)
Let
\( f(x) = x^2 - 5x \quad \text{and} \quad g(x) = 7x - x^2 \)
To find the area enclosed between these curves, we calculate:
\( \int_0^6 (g(x) - f(x)) \, dx = \int_0^6 ((7x - x^2) - (x^2 - 5x)) \, dx \)
Simplify the integrand:
\( = \int_0^6 (12x - 2x^2) \, dx \)
Now, integrate term by term:
\( = \left[ \frac{12x^2}{2} - \frac{2x^3}{3} \right]_0^6 \)
Substitute the limits:
\( = (6 \cdot 6^2) - \frac{2}{3} \cdot (6)^3 \)
\( = 216 - 144 = 72 \, \text{unit}^2 \)
Let the area of the bounded region $ \{(x, y) : 0 \leq 9x \leq y^2, y \geq 3x - 6 \ be $ A $. Then 6A is equal to:
20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)