JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q76

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MathematicsSingle correct+4 / -1Question 76 of 90

The area (in sq. units) of the region described by $A=\{(x,y)\mid y\ge x^2-5x+4,\ x+y\ge1,\ y\le0\}$ is :

\dfrac72

\dfrac{19}6

\dfrac{13}6

\dfrac{17}6

Answer and worked solution

Official answer: B

The line meets the parabola at x = 1 and 3. Below the x-axis the region is bounded by the line for $1\le x\le3$ and by the parabola for $3\le x\le4$ :
$\int_1^3(x-1)\,dx+\int_3^4-(x^2-5x+4)\,dx=2+\frac76=\frac{19}6.$

Topics:Area between curves

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 76