Question

A curve passes through (0,1),(1.1.5), (2,3) then the value of ​

Answer 1

Answer: The value of definite integral is 4.

Given: Three points (0,1), (1,1.5), (2,3).

To Find:

$\int\limits^2_0 {y \, dx$ by using Trapezoidal rule.

Step-by-step explanation:

Step 1: Trapezoidal rule is used to find the approximate value of definite integrals. In calculus it can be describe as given,

$\int\limits^b_a {f(x)} \, dx \approx (b-a).\frac{1}{2}.(f(a)+f(b))$

Here, $a=0, b=2$. Now using the given co-ordinate we can find out the values of function at point 0 and 2, which are given below.

$f(0)=1\\f(2)=3$

Step 2: Now, by putting the values in the above formula we can find out the definite integral as given below

$\int\limits^2_0 {f(x)} \, dx \approx (2-0).\frac{1}{2}.(f(0)+f(2))\\\int\limits^2_0 {f(x)} \, dx \approx (1+3)\\\\\int\limits^2_0 {f(x)} \, dx \approx 4$

So, we can say that by using Trapezoidal rule the value of given definite integral is 4.

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