Application of Integrals

CBSE Class 12 · Mathematics · 13 past questions

1. Q1 2026

   The area bounded by the curve $y = x|x|$, $x$-axis and the ordinates $x = -1$ and $x = 1$ is given by

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2. Q2 2026

   Which of the following expressions will give the area of region bounded by the curve $y=x^2$ and line $y=16$ ?

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3. Q3 2025

   Sketch the graph of $y = |x+3|$ and find the area of the region enclosed by the curve, $x$-axis, between…

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4. Q4 2025

   Using integration, find the area of the region bounded by the line $y = 5x + 2$, the $x$-axis and the…

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5. Q5 2025

   The area of the region enclosed by the curve $y = \sqrt{x}$ and the lines $x = 0$ and $x = 4$ and x-axis is…

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6. Q6 2025

   Calculate the area of the region bounded by the curve $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ and the x-axis using…

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7. Q7 2024

   Using integration, find the area of the ellipse $\frac{x^2}{16} + \frac{y^2}{4} = 1$, included between the…

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8. Q8 2024

   Using integration, find the area of the region enclosed between the circle $x^2 + y^2 = 16$ and the lines…

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9. Q9 2024

   If $A_1$ denotes the area of region bounded by $y^2 = 4x$, $x = 1$ and x-axis in the first quadrant and $A_2$…

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10. Q10 2023

    The area of the region bounded by the line $y = mx$ ($m > 0$), the curve $x^2 + y^2 = 4$ and the x-axis in…

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11. Q11 2023

    Find the area of the region bounded by the curves $x^2 = y$, $y = x + 2$ and x-axis, using integration.

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12. Q12 2023

    Using integration, find the area of region bounded by line $y=\sqrt3x$, the curve $y=\sqrt{4-x^2}$ and y–axis…

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13. Q13 2022

    Using integration, find the area of the region $\{(x,y):4x^2+9y^2\le36,\ 2x+3y\ge6\}$.

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