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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: Using the definite integration area of the circle x2 + y2 = 16 is ______

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प्रश्न

Choose the correct alternative:

Using the definite integration area of the circle x2 + y2 = 16 is ______

पर्याय

  • 4π sq.units

  • 4 sq.units

  • 16 sq.units

  • 16π sq.units

MCQ
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उत्तर

16π sq.units

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.7: Application of Definite Integration - Q.1 (A)

संबंधित प्रश्‍न

Find the area of the region bounded by the ellipse  `x^2/16 + y^2/9 = 1.`


The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.


Find the area bounded by the curve x2 = 4y and the line x = 4y – 2


Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.


Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .


Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.


Find the area of the region bounded by the following curves, the X-axis and the given lines:

y = x2 + 1, x = 0, x = 3


Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.


Fill in the blank :

Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.


Fill in the blank :

The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.


State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.


Solve the following :

Find the area of the region bounded by the curve y = x2 and the line y = 10.


State whether the following statement is True or False:

The area of portion lying below the X axis is negative


State whether the following statement is True or False:

The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x)  "d"x| + |int_"b"^"c" "f"(x)  "d"x|`


The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`


Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant


If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?


`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.


The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.


Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.


The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.


Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.


The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.


The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.


Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.


Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?


Why is the area enclosed by \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] written as \[4\int_0^a y\,dx\]?


Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?


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