Class 12

Math

Calculus

Application of Integrals

If the area of the region ${(x,y):0≤y≤x_{2}+1,0≤y≤x+1,0≤x≤2}$ is $A$ , then the value of $3A−17$ is____

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Smaller area enclosed by the circle $x_{2}+y_{2}=4$and the line $x+y=2$is(A) $2(π−2)$ (B) $π−2$ (C) $2π−1$ (D) $2(π+2)$

The area bounded by the curve $y=x∣x∣$, x-axis and the ordinates $x=−1$and $x=1$is given by(A) 0 (B) $31 $ (C) $32 $ (D) $34 $[Hint : $y=x_{2}$if $x>0$and $y=−x_{2}$if $x<0$].

Using integration find the area of region bounded by the triangle whose vertices are $(1,0),(1,3)and(3,2)$.

Find the area bounded by curves $(x−1)_{2}+y_{2}=1$and $x_{2}+y_{2}=1$.

If the area of bounded between the x-axis and the graph of $y=6x−3x_{2}$ between the ordinates $x=1$ and $x=a$ is $19$ units, then $a$ can take the value: (A) 4 or -2 (B) one value is in (2, 3) and one in (-1, 0) (C) one value is in (3, 4) and one in (-2,-1) (D) none of these

Find the area bounded by the curve $y=cosx$between $x=0$and $x=2π$.

Consider two curves $C_{1}:y_{2}=4[y ]xandC_{2}:x_{2}=4[x ]y,$ where [.] denotes the greatest integer function. 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 $38 squ˙nits$ (b) $310 squ˙nits$ $311 squ˙nits$ (d) $411 squ˙nits$

Area bounded by the curve $y=x_{3}$, the x-axis and the ordinates $x=2$and $x=1$is(A) $−9$ (B) $4−15 $ (C) $415 $ (D) $417 $