Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]

\[\int\limits_0^2 \left( x^2 + 2 \right) dx\]

\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]

If  \[\vec{a} \text{ and } \vec{b}\] are two non-collinear unit vectors such that \[\left| \vec{a} + \vec{b} \right| = \sqrt{3},\] find \[\left( 2 \vec{a} - 5 \vec{b} \right) \cdot \left( 3 \vec{a} + \vec{b} \right) .\] 

Find : `∫_a^b logx/x` dx

Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`

Prove that : `2sin^-1 (3/5) -tan^-1 (17/31) = pi/4.`

The function f(x) = `{{:(sinx/x + cosx",",  "if" x ≠ 0),("k"",",  "if" x = 0):}` is continuous at x = 0, then the value of k is ______.

The derivative of sin x w.r.t. cos x is ______.

If f(x) = |cosx|, then `"f'"(pi/4)` = ______.

If f(x) = |cosx – sinx| , then `"f'"(pi/4)` = ______.

Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x

Evaluate `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`

Evaluate `int sqrt((1 + x)/(1 - x)) "d"x`, x ≠1

Find `int x^2/(x^4 + 3x^2 + 2) "d"x`

Evaluate `int "dx"/sqrt((x - alpha)(beta - x)), beta > alpha`

Find `int sqrt(10 - 4x + 4x^2)  "d"x`

Evaluate `int (x^2"d"x)/(x^4 + x^2 - 2)`

Evaluate `int (x^2 + x)/(x^4 - 9) "d"x`

If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4e^x + 5e –x| + C, then ______.