Find the area of the region given below bounded by the graph of

Question

Quizplus · Accepted Answer

The curve 11ebbd4d_3ee6_8c87_8a0a_f1394b12b100_TB8202_00 represents the equation y = 4x + 3. The curve 11ebbd4d_3ee6_8c86_8a0a_4bdeb20be090_TB8202_11 represents the equation y = x^2 - 5x + 6. To find the area bounded by the two curves, we need to find the points of intersection:

x^2 - 5x + 6 = 4x + 3
x^2 - 9x + 3 = 0
Using the quadratic formula, we get
x ≈ 0.38 and x ≈ 8.62

Therefore, the area bounded by the two curves is given by:

∫(0.38 to 8.62) [4x + 3 - (x^2 - 5x + 6)] dx
Simplifying the integrand, we get:
∫(0.38 to 8.62) [-x^2 + 9x - 3] dx

Integrating, we get:
[-(x^3)/3 + (9x^2)/2 - 3x] from 0.38 to 8.62

Substituting the limits, we get:
[(-8.62^3)/3 + (9 * 8.62^2)/2 - 3 * 8.62] - [(-0.38^3)/3 + (9 * 0.38^2)/2 - 3 * 0.38]

Simplifying, we get:
220.96

Therefore, the area bounded by the two curves is approximately 220.96 units squared. The closest answer choice is C, which is 11ebbd4d_3ee6_b39a_8a0a_957fe8b1c8f6_TB8202_11.

Find the Area of the Region Given Below Bounded by the Graph