Advertisements
Advertisements
प्रश्न
Evaluate: ∫ x . log x dx
Advertisements
उत्तर
Let ∫ x . log x dx
= ∫ log x . x . dx ...[by LIATE rule]
Integrating by parts
I = `"log x" . int "x" "dx" - int ["d"/"dx" ("log x") int "x" "dx"] "dx"`
`= "log x" . ("x"^2/2) - int 1/"x" . ("x"^2/2) "dx"`
`= "x"^2/2 . "log x" - 1/2 int "x" "dx"`
`= "x"^2/2 . "log x" - 1/2 ("x"^2/2) + "c"`
`= "x"^2/2 . "log x" - "x"^2/4" + c`
APPEARS IN
संबंधित प्रश्न
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
Milk is white or grass is green.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Find the truth value of the following statement.
3 is a prime number and an odd number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ∨ (r ∧ s)
Negation of “some men are animal” is ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
To be brave is necessary and sufficient condition to climb the Mount Everest.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Negation of p → (p ˅ ∼ q) is ______
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Write the negation of p → q
Which of the following is NOT true for p → q.
Let p, q and r be any three logical statements. Which of the following is true?
