Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Integrals

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Multiple Choice Questions

81.

Area lying between the curves y² = 4x and y = 2x is

$2 over 3$
$1 third$
$1 fourth$
$1 fourth$

196 Views

82. Area bounded by the curve y = x³ the x-axis and the ordinates x - 2 and a = 1 is

-9
$fraction numerator negative 15 over denominator 4 end fraction$
$15 over 4$
$15 over 4$

110 Views

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

0

$1 third$
$2 over 3$
$2 over 3$

2 over 3

We want to find the area bounded by the curve $straight y equals straight x space open vertical bar straight x close vertical bar comma$ x-axis and the ordinates x = -1 and x = 1
Required area = $integral subscript negative 1 end subscript superscript 1 space straight y space dx space equals space integral subscript negative 1 end subscript superscript 1 space straight x space open vertical bar straight x close vertical bar space dx$
$equals space integral subscript negative 1 end subscript superscript 0 open vertical bar straight x open vertical bar straight x close vertical bar close vertical bar space dx space plus space integral subscript 0 superscript 1 space straight x space open vertical bar straight x close vertical bar space dx$
$open square brackets because space space space open vertical bar straight x space open vertical bar straight x close vertical bar close vertical bar space equals space open vertical bar straight x close vertical bar space open vertical bar straight x close vertical bar space equals straight x squared close square brackets$
$equals space integral subscript negative 1 end subscript superscript 0 left parenthesis straight x squared right parenthesis dx plus integral subscript 0 superscript 1 straight x squared dx space equals space open square brackets straight x cubed over 3 close square brackets subscript negative 1 end subscript superscript 0 plus open square brackets straight x cubed over 3 close square brackets subscript 0 superscript 1 equals space open square brackets 0 minus fraction numerator left parenthesis negative 1 right parenthesis cubed over denominator 3 end fraction close square brackets plus open square brackets 1 third minus 0 close square brackets space equals space 1 third plus 1 third equals 2 over 3$

122 Views

84. The area of the circle x +y =16 exterior to the parabola y² = 6x is

$4 over 3 left parenthesis 4 straight pi minus square root of 3 right parenthesis$
$4 over 3 left parenthesis 4 straight pi plus square root of 3 right parenthesis$
$4 over 3 left parenthesis 8 straight pi minus square root of 3 right parenthesis$
$4 over 3 left parenthesis 8 straight pi minus square root of 3 right parenthesis$

196 Views

85.

The area bounded by the x-axis, y = cosx and y = sin x when $0 less or equal than straight x less or equal than straight pi over 2$

$2 left parenthesis square root of 2 minus 1 right parenthesis$
$square root of 2 minus 1$
$square root of 2 plus 1$
$square root of 2 plus 1$

162 Views

Long Answer Type

86. Prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.

640 Views

87.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

1133 Views

88.

Sketch the region bounded by the curves $straight y equals square root of 5 minus straight x squared end root space and space straight y space equals open vertical bar straight x minus 1 close vertical bar$ and find its area using integration.

600 Views

89.

Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5) and (3, 4).

363 Views

90.

Using integration, find the area bounded by the curve x² = 4y and the line x = 4y – 2.

350 Views