Class 12

Math

Calculus

Area

The value of $a(a>0)$ for which the area bounded by the curves $y=6x +x_{2}1 ,y=0,x=a,andx=2a$ has the least value is ___.

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Find the area of the region bounded by the curves $y=x+2 andy=x+11 $ between the lines x=0 and x=2.

The area of the region bounded by $x_{2}+y_{2}−2x−3=0andy=∣x∣+1$ is

Let function f(x) is defined in $[−2,2]$ as $f(x)=⎩⎨⎧ {x},∣sgnx∣,{−x}, −2≤x≤−1−1≤x≤11<x≤2 $ where {x} and sgn x denotes fractional part and signum functions, respectively. Then the area bounded by the graph of f(x) and x-axis is

The area of the region enclosed by the curves $y=x,x=e,y=x1 $ and the positive x-axis is

Find the smallest area bounded by the curves $y=x−sinx,y=x+cosx.$

If $(a,0)$, agt 0, is the point where the curve $y=sin2x−3 sinx$ cuts the x-axis first, A is the area bounded by this part of the curve, the origin and the positive x-axis. Then

The area bounded by the curves $y=xe_{x},y=xe_{−x}$ and the line x=1 is

The area enclosed between the curve $y=sin_{2}xandy=cos_{2}x$ in the interval $0≤x≤π$ is