The slope of tangent to the curve y=f(x) at (x, f(x)) is (2 x+1). If the curve passes through the point (1,2), then the area bounded by the curve the x-axis and line x=1 is

Question

The slope of tangent to the curve y=f(x) at (x, f(x)) is (2 x+1). If the curve passes through the point (1,2), then the area bounded by the curve the x-axis and line x=1 is (A) (5/6) (B) (6/5) (C) (1/6) (D) 6

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a9bcce12467d997990a5f5e48597f076-.png" /> ( dy / dx )=2 x +1 y=x2+x+C 2=2+C ⇒ C=0 y=x2+x text Area =∫ limits01(x2+x) d x=(1/3)+(1/2)=(5/6) .

Q. The slope of tangent to the curve $y = f (x)$ at $(x, f (x))$ is $(2 x + 1)$ . If the curve passes through the point $(1, 2)$ , then the area bounded by the curve the $x$ -axis and line $x = 1$ is

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{1}{6}$

6

$\frac{d y}{d x} = 2 x + 1$
$y = x^{2} + x + C$
$2 = 2 + C \Rightarrow C = 0$
$y = x^{2} + x$
$Area = 0 \int 1 (x^{2} + x) d x = \frac{1}{3} + \frac{1}{2} = \frac{5}{6} .$

Q. The slope of tangent to the curve y=f(x) at (x,f(x)) is (2x+1). If the curve passes through the point (1,2), then the area bounded by the curve the x-axis and line x=1 is

65​

56​

61​

6

dxdy​=2x+1 y=x2+x+C 2=2+C⇒C=0 y=x2+x Area =0∫1​(x2+x)dx=31​+21​=65​.

Q. The slope of tangent to the curve $y = f (x)$ at $(x, f (x))$ is $(2 x + 1)$ . If the curve passes through the point $(1, 2)$ , then the area bounded by the curve the $x$ -axis and line $x = 1$ is

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{1}{6}$

$\frac{d y}{d x} = 2 x + 1$
$y = x^{2} + x + C$
$2 = 2 + C \Rightarrow C = 0$
$y = x^{2} + x$
$Area = 0 \int 1 (x^{2} + x) d x = \frac{1}{3} + \frac{1}{2} = \frac{5}{6} .$