Properties of integrals Suppose that ∫ 1 4 f ( x ) d x = 6 , and ∫ 1 4 g ( x ) d x = 4 , and ∫ 3 4 f ( x ) d x = 2 . Evaluate the following integrals or state that there is not enough information. 39. ∫ 1 4 3 f ( x ) d x
Properties of integrals Suppose that ∫ 1 4 f ( x ) d x = 6 , and ∫ 1 4 g ( x ) d x = 4 , and ∫ 3 4 f ( x ) d x = 2 . Evaluate the following integrals or state that there is not enough information. 39. ∫ 1 4 3 f ( x ) d x
Solution Summary: The author evaluates the value of integral displaystyle 'underset' 1overset4int.
Properties of integralsSuppose that
∫
1
4
f
(
x
)
d
x
=
6
, and
∫
1
4
g
(
x
)
d
x
=
4
, and
∫
3
4
f
(
x
)
d
x
=
2
. Evaluate the following integrals or state that there is not enough information.
39.
∫
1
4
3
f
(
x
)
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
3. Consider the initial value problem
9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1.
Solve the problem and find the value of a such that the solution of the initial value problem is always
positive.
5. Euler's equation.
Determine the values of a for which all solutions of the equation
5
x²y" + axy' + y = 0
that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.
4. Problem on variable change.
The purpose of this problem is to perform an appropriate change of variables in order to reduce
the problem to a second-order equation with constant coefficients.
ty" + (t² − 1)y'′ + t³y = 0, 0
Chapter 5 Solutions
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY