help@askiitians.com

1800-150-456-789

Integral Calculus> The slope of the tangent to a curve y=f(x...

question mark

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

Vivek , 10 Years ago

Grade 12th pass

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

Slope of the curve at any point x
$\frac{df(x)}{dx} = 2x + 1$
$df(x) = (2x + 1)dx$
Integrate both sides
$\int df(x) = \int (2x + 1)dx$
$f(x) = x^{2} + x + c$
It is passing through (1, 2)
$2 = 1^{2} + 1 + c$
$\Rightarrow c = 0$
$f(x) = x^{2} + x$
Area bounded by curve in the given region:
$I = \int_{0}^{1}(x^{2}+x)dx$
$I = (\frac{x^{3}}{3}+\frac{x^{2}}{2})_{0}^{1}$
$I = (\frac{1}{3}+\frac{1}{2})$
$I = \frac{5}{6}$

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

The area of a square field is 640000cm2.what is its area in hectares

Integral Calculus

1 Answer Available

Last Activity: 2 Years ago

Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request

Integral Calculus

0 Answer Available

Last Activity: 2 Years ago

Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0

Integral Calculus

0 Answer Available

Last Activity: 2 Years ago

how to solve this?this is interger type question .

Integral Calculus

0 Answer Available

Last Activity: 2 Years ago

Integrate 0 to π/2 (x sin x cos x )/(a²cos²x + b²sin²x)²

Integral Calculus

1 Answer Available

Last Activity: 2 Years ago

View all Questions