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Application of Integrals

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Applications in finding the area under simple curves (lines, circles, parabolas, ellipses)

Subtopic

Applications in finding the area under simple curves (lines, circles, parabolas, ellipses) under Application of Integrals for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the area of the region bounded by the line y=2y = 2, the xx-axis, and the ordinates x=1x = 1 and x=3x = 3.

    A.

    2 sq units

    B.

    4 sq units

    C.

    6 sq units

    D.

    1 sq unit

  2. 2.

    The area bounded by y=∣x∣y = |x|, the xx-axis, and the lines x=−1x = -1 and x=1x = 1 is:

    A.

    12\frac{1}{2} sq units

    B.

    1 sq unit

    C.

    2 sq units

    D.

    23\frac{2}{3} sq units

  3. 3.

    Find the area of the region bounded by y=4−xy = \sqrt{4 - x}, the xx-axis, and the yy-axis.

    A.

    163\frac{16}{3} sq units

    B.

    83\frac{8}{3} sq units

    C.

    4 sq units

    D.

    323\frac{32}{3} sq units

Download the worksheet for Application of Integrals - Applications in finding the area under simple curves (lines, circles, parabolas, ellipses) to practice offline. It includes additional chapter-level practice questions.

Area between any of the two above said curves

Subtopic

Area between any of the two above said curves under Application of Integrals for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the area of the region bounded by the curve y2=xy^2 = x and the line y=12xy = \frac{1}{2} x.

    A.

    23\frac{2}{3} sq unit

    B.

    83\frac{8}{3} sq units

    C.

    43\frac{4}{3} sq units

    D.

    2 sq units

  2. 2.

    Determine the area bounded by the curve y=5x4y = 5x^4 and the xx-axis from x=0x = 0 to x=1x = 1.

    A.

    5 sq units

    B.

    1 sq unit

    C.

    15\frac{1}{5} sq unit

    D.

    54\frac{5}{4} sq units

  3. 3.

    The area of the region bounded by y=sec⁡2xy = \sec^2 x, the xx-axis and the lines x=0,x=π4x = 0, x = \frac{\pi}{4} is:

    A.

    π\pi sq units

    B.

    12\frac{1}{2} sq unit

    C.

    1 sq unit

    D.

    2\sqrt{2} sq units

Download the worksheet for Application of Integrals - Area between any of the two above said curves to practice offline. It includes additional chapter-level practice questions.