What is ^ _0 ln(tanx/2) dx equal to?
The logic is straightforward: solving fully: apply relevant formula, put numbers, compute. Result comes as 0. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Integrals
Integral Calculus 1
Integral Calculus 1 covers the basics of antiderivatives, definite integrals, and common techniques of integration. The category provides practice questions and step‑by‑step solutions to help students build a solid foundation in integral calculus.
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e^x f( x ) + f'( x ) dx; is equal to
We know that complete solution: write formula, plug data, do arithmetic. Final value matches e^xf( x ) +C. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
If xdy/dx=y( y- x+1) , then the solution of the equation is
In easy words, complete solution: write formula, plug data, do arithmetic. Final value matches y/x=Cx. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
If f(x) = 2x, then what is ^10_2f'(x)/f(x)dx equal to?
From the definition, after simplifying, 8 ln 2 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Integrals
What is value of _-/2^/2 x^5^4x dx ?
The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as 0. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Integrals
Suppose, I = d/dx _ x^ x 1/t dt , Then which of the following is the correct value of this given definite integral?
The trick is using formula we get - tan x - cot x. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get - tan x - cot x.
Ref: NCERT Mathematics Class XII — Integrals
If f(2a - x) = f(x) and ^a_0f(x)dx= then ^2a_0f(x)dx is:
We know that complete solution: write formula, plug data, do arithmetic. Final value matches 2λ. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
Find the value of a + b if _0^1 dtt^2+25=1/5(tan^-1b-tan^-1a)
Here's the idea in simple terms: solving fully: apply relevant formula, put numbers, compute. Result comes as 1/5. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Integrals
What is the value of _-/2^/2| x|:dx?
The trick is we verify 2 by full calculation: use standard identity, substitute, simplify step by step to reach 2.
Ref: NCERT Mathematics Class XII — Integrals
What is ^/2_0 e^ln(cos x) dx equal to?
Let's break it down: complete solution: write formula, plug data, do arithmetic. Final value matches 1. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
_0^ /31+ 2x, dx
Look at it this way: after simplifying, 3+12 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Integrals
1/c _ac^bcf(x/c)dx is equal to
From the definition, we verify _a^b f(x)dx by full calculation: use standard identity, substitute, simplify step by step to reach _a^b f(x)dx.
Ref: NCERT Mathematics Class XII — Integrals
