If the area enclosed by g(x), x=-3, x=5 and x-axis where g(x) is the inverse of f(x)=x3+3 x+1 is A, then [A] equals [Note: [k] denotes the greatest integer function less than or equal to k.]

Question

If the area enclosed by g(x), x=-3, x=5 and x-axis where g(x) is the inverse of f(x)=x3+3 x+1 is A, then [A] equals [Note: [k] denotes the greatest integer function less than or equal to k.] (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d1dc57b0f95bfab86523736fa4be6cf8-.png" /> Area =∫ limits-10((x3+3 x+1)-(-3)) d x+∫ limits01(5-(x3+3 x+1)) d x=(9/2)

Q. If the area enclosed by $g (x), x = - 3, x = 5$ and $x$ -axis where $g (x)$ is the inverse of $f (x) = x^{3} + 3 x + 1$ is $A$ , then $[A]$ equals
[Note: [k] denotes the greatest integer function less than or equal to $k$ .]

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5

Area $= - 1 \int 0 ((x^{3} + 3 x + 1) - (- 3)) d x + 0 \int 1 (5 - (x^{3} + 3 x + 1)) d x = \frac{9}{2}$

Q. If the area enclosed by g(x),x=−3,x=5 and x-axis where g(x) is the inverse of f(x)=x3+3x+1 is A, then [A] equals [Note: [k] denotes the greatest integer function less than or equal to k.]

2

3

4

5

Area =−1∫0​((x3+3x+1)−(−3))dx+0∫1​(5−(x3+3x+1))dx=29​

Q. If the area enclosed by $g (x), x = - 3, x = 5$ and $x$ -axis where $g (x)$ is the inverse of $f (x) = x^{3} + 3 x + 1$ is $A$ , then $[A]$ equals
[Note: [k] denotes the greatest integer function less than or equal to $k$ .]

Area $= - 1 \int 0 ((x^{3} + 3 x + 1) - (- 3)) d x + 0 \int 1 (5 - (x^{3} + 3 x + 1)) d x = \frac{9}{2}$