Applications Of Integrals Questions for CBSE Class 12th

# Applications Of Integrals Questions for CBSE Class 12th

Find the area, lying above the x -axis and included between the circle x 2 + y 2 = 8 x and the parabola y 2 = 4 x

The area of the region bounded by the curves y = 3 − | x | and y = | x − 1 | is

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The area(in sq. units) of the region x , y ∈ R 2 | 4 x 2 ≤ y ≤ 8 x + 12 is

Evaluate ∫ 0 2 π [ sin ⁡ x ] d x , where [.] denotes the greatest integer function.

If ∫ 0 1 e − x d x 1 + e x = log e ⁡ ( 1 + e ) + K , then find the value of k is

Find the area bounded by y = x 3 − x and y = x 2 + x

If the area enclosed by curve y = f ( x ) and y = x 2 + 2 between the abscissa x = 2 and x = α , α > 2 , is α 3 − 4 α 2 + 8 sq. unit. It is known that curve y = f ( x ) lies below the parabola y = x 2 + 2

The area bounded by y = sin − 1 ⁡ x ; y = cos − 1 ⁡ x , and the x -axis.

The area bounded by y = 1 x 2 − 2 x + 2 and x -axis.

The area bounded by y = log e ⁡ | x | and y = 0

The area bounded by the curves y = x 2 − 2 x + 2 ; x ≥ 1 and its inverse is given by

A curve y = f ( x ) which passes through ( 4 , 0 ) satisfies the differential equation x d y + 2 y d x = x ( x − 3 ) d x . The area bounded by y = f ( x ) and line y = x (in square unit) is

The maximum possible area bounded by the curves y = cos ⁡ x , y = x + 1 , y = 0 is

Slope of normal to a curve y = f ( x ) at any point on curve is x y and curve is passing through the point ( 1 , 1 ) . Then area formed by y = f ( x ) , x – axis x = 3 and x = 5 is

The area (in square units) bounded by the region inside the circle x 2 + y 2 = 36 and outside the parabola y 2 = 9 x is

The area of the region, enclosed by the circle x 2 + y 2 = 2 which is not common to the region bounded by the parabola y 2 = x and the straight line y = x, is:

For a > 0 , let the curves C 1 : y 2 = ax and C 2 : x 2 = ay intersect at origin O and a point P . Let the line x = b ( 0 < b < a ) intersect the chord OP and the x -axis at points Q and R , respectively. If the line x = b bisects the area bounded by the curves, C 2 and C , and the area of Δ OQR = 1 2 , then ‘a’ satisfies the equation:

The area of the region ( x , y ) : 0 ≤ y ≤ x 2 + 1 , 0 ≤ y ≤ x + 1 , 0 ≤ x ≤ 2 is

Consider two curves C 1 : y 2 = 4 [ y ] x and C 1 : x 2 = 4 [ x ] y , where [ . ] denotes G.I.F then the area of region enclosed by these two curves within the square formed by the lines x = 1 , y = 1 , x = 4 & y = 4 is

Area of the figure bounded by y ≤ 3 – | 3 – x | and y ≥ | x – 3 | is equal to

If f ( x ) = min | x | , 1 − | x | , 1 4 ∀ x ∈ R then find the value of ∫ − 1 1 f ( x ) d x .

If y = ∫ x 2 x 3 1 log ⁡ t d t (where x > 0 ), then find d y d x

Area bounded by the curves y = sin ⁡ x and y = cos ⁡ x between two consecutive points of the intersection.

The area of the region ( x , y ) : y 2 ≤ 4 x , 4 x 2 + 4 y 2 ≤ 9

T h e a r e a o f t h e r e g i o n b o u n d e d b y y = ∥ log e ⁡ ⌊ x ∥ and y = 0

The area of the region enclosed between the curves x = y 2 − 1 and x = | y | 1 − y 2 is – – – – – – sq. units

If x = a divides the area bounded by x – axis, part of the curve y = 1 + 8 x 2 and the ordinates x = 2 , x = 4 into equal parts then a =

The area bounded by the loop of 4 y 2 = x 2 4 − x 2 is

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