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 that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
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.
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is a holiday and Ram studies on holiday.
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
