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12th Standard English Medium Maths Subject Applications of Integration Book Back 5 Mark Questions with Solution Part - I

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Estimate the value of \(\int _{ 0 }^{ 0.5 }{ { x }^{ 2 } } dx\) using the Riemann sums corresponding to 5 subintervals of equal width and applying
    (i) left-end rule
    (ii) right-end rule
    (iii) the mid-point rule.

  2. Evaluate\(\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }+3) } \) dx, as the limit of a sum

  3. Show that \(\int ^{1}_{0} (tan ^{-1} x + tan ^{-1}(1-x))\) dx = \(\frac {\pi}{2}\) - loge

  4. Find the area of the region bounded by y = cos x, y = sin x, the lines x = \(\frac{\pi}{4}\) and x = \(\frac{5\pi}{4}\).

  5. The curve y = (x − 2)+1 has a minimum point at P. A point Q on the curve is such that the slope of PQ is 2. Find the area bounded by the curve and the chord PQ.

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