# Q. The area of the region above X-axis included between the parabola $y^2 = x$ and the circle $x^2 + y^2 = 2x$ in square units is

KCET KCET 2019Application of Integrals

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## $y^{2}=x \quad\to\left(1\right)$ $x^{2}+y^{2}=2x\quad\to\left(2\right)$ Equation (2) is a circle with centre (1, 0) and radius 1. Solving (1) and (2), we get the points of intersection (0, 0) and (1, 1) $\left(x-1\right)^{2}+y^{2}=1$ $y^{2}=x$ $\left(x-1\right)^{2}+x=1$ $x^{2}-x=0$ $x\left(x-1\right)=0$ $x=0, x=1$ $area =\int\limits_{0}^{1} \left\{\sqrt{1-\left(x-1\right)^{2}}-\sqrt{x}\right\}dx$ $=-\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]_{0}^{1}+\left[\frac{x-1}{2}\sqrt{1-\left(x-1\right)^{2}}+\frac{1}{2}sin^{-1}\left(x-1\right)\right]_{0}^{1}$ $=-\frac{2}{3}+\left\{0+\frac{\pi}{4}\right\}=-\frac{2}{3}+\frac{\pi}{4}$

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## 2. If $3A + 4B' = $$\begin{bmatrix}7&-10&17\\ 0&6&31\end{bmatrix} and 2B - 3A' \begin{bmatrix}-1&18\\ 4&0\\ -5&-7\end{bmatrix} then B = ## 3. If A = \begin{bmatrix}1&3\\ 4&2\end{bmatrix} , B = \begin{bmatrix}2&-1\\ 1&2\end{bmatrix} , Then | ABB'| = ## 4. If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is ## 5. \int x^{3} \sin 3x dx = ## 6. The area of the region bounded by Y-axis, y = cos x and y = sin x 0 \le x \le \frac{\pi}{2} is ## 7. The integrating factor of the differential equation (2x + 3y^2) dy = y \,dx (y > 0) is ## 8. The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is ## 9. Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2x - y + z + 3 = 0 is ## 10. Acute angel between the line \frac{x-5}{2} = \frac{y+1}{-1} = \frac{z+4}{1} and the plane 3x - 4y - z + 5 = 0 is ## Questions from Application of Integrals ## 1. f(x ) = minimum of \{x-[x],-x-[-x]\} and x = +2 then the area of f(x) in sq.units ## 2. The area of the region bounded by 3x \pm 4y \pm 6 = 0 in sq. units ## 3. The area of the region bounded by \sqrt{x} + \sqrt{y} = 1 in the first quadrant is ## 4. The area in square units of the region bounded by the curve x^2 = 4 \,y , the fine x=2 and the X-axis is EAMCET 2000 ## 5. The area bounded by the parabola y^2 = 4x and its latusrectum is ## 6. The area of the region bounded by y = \sin^4\, x , X-axis and ordinates x = 0 , x = 2\pi (in sq. units) ## 7. The area bounded by the curve y = 7x -10 - x^2 with X-axis is ## 8. The area bounded by the curve y = ( x - 4 ) ( x - 1) and the X-axis is ## 9. The area between the curve y = (x - 1 )^2 - 25 and X-axis in sq. units is ## 10. The area bounded by y = x^2 + 2, X-axis, x=1 and x=2 is ## Mathematics Most Viewed Questions ## 1. The number of terms in the expansion of (x^2 +y^2 )^{25} - (x^2 - y^2)^{25} after simplification is KCET 2019 Binomial Theorem ## 2. The locus represented by xy + yz = 0 is KCET 2018 Three Dimensional Geometry ## 3. Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2x - y + z + 3 = 0 is KCET 2019 Three Dimensional Geometry ## 4. If ^nC_{12}= ^nC_{6} then ^nC_{2}=......... KCET 2005 Permutations and Combinations ## 5. If P and Q are symmetric matrices of the same order then PQ - QP is KCET 2019 Matrices ## 6. The area of the region bounded by Y-axis, y = cos x and y = sin x 0 \le x \le \frac{\pi}{2} is KCET 2019 Application of Integrals ## 7. \int x^{3} \sin 3x dx = KCET 2019 Integrals ## 8. If 3A + 4B' =$$\begin{bmatrix}7&-10&17\\ 0&6&31\end{bmatrix}$ and $2B - 3A'$ $\begin{bmatrix}-1&18\\ 4&0\\ -5&-7\end{bmatrix}$ then $B =$

KCET 2019 Matrices

## 9. On the set of positive rationals, a binary operation * is defined by a * b = $\frac{2ab}{5}$ . If 2 * x = $3^{-1}$ then x =

KCET 2019 Relations and Functions

## 10. The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

KCET 2019 Differential Equations