Match the following, where [.] greatest integer functionA∫−11[x+[x+[x]]]dxP–6B2∫25([x]+[−x])dxQ1/5C∫0π/4(tan6(x−[x])+tan4(x−[x]))dxR–3D∫−13sgn(x−[x])dxS4 T–4

A)∫−10[x+[x−1]]dx+∫01[x+[x+0]]dx=−3+0=−3B) 2∫25([x]+[−x])dx=2[−1−1−1]=−6C)∫0π/4tan4x.sec2xdx=15D) ∫−13sgn(x−(−x))dx=3+1=4

Match the following, where [.] greatest integer functionA∫−11[x+[x+[x]]]dxP–6B2∫25([x]+[−x])dxQ1/5C∫0π/4(tan6(x−[x])+tan4(x−[x]))dxR–3D∫−13sgn(x−[x])dxS4 T–4

A)∫−10[x+[x−1]]dx+∫01[x+[x+0]]dx=−3+0=−3B) 2∫25([x]+[−x])dx=2[−1−1−1]=−6C)∫0π/4tan4x.sec2xdx=15D) ∫−13sgn(x−(−x))dx=3+1=4

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Match the following, where $[.]$ greatest integer function
A
$\int_{- 1}^{1} [x + [x + [x]]] d x$
P
–6
B
$2 \int_{2}^{5} ([x] + [- x]) d x$
Q
1/5
C
$\int_{0}^{π / 4} (\tan^{6} (x - [x]) + \tan^{4} (x - [x])) d x$
R
–3
D
$\int_{- 1}^{3} sgn (x - [x]) d x$
S
4

T
–4

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$A \to P, B \to Q, C \to R, D \to S$

$A \to Q, B \to P, C \to S, D \to R$

$A \to S, B \to Q, C \to P, D \to R$

$A \to R, B \to P, C \to Q, D \to S$

answer is A.

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Detailed Solution

$A) \int_{- 1}^{0} [x + [x - 1]] d x + \int_{0}^{1} [x + [x + 0]] d x = - 3 + 0 = - 3$

$B) 2 \int_{2}^{5} ([x] + [- x]) d x = 2 [- 1 - 1 - 1] = - 6$

$C) \int_{0}^{π / 4} \tan^{4} x . \sec^{2} x d x = \frac{1}{5}$

$D) \int_{- 1}^{3} sgn (x - (- x)) d x = 3 + 1 = 4$

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A	$\int_{- 1}^{1} [x + [x + [x]]] d x$	P	–6
B	$2 \int_{2}^{5} ([x] + [- x]) d x$	Q	1/5
C	$\int_{0}^{π / 4} (\tan^{6} (x - [x]) + \tan^{4} (x - [x])) d x$	R	–3
D	$\int_{- 1}^{3} sgn (x - [x]) d x$	S	4
		T	–4

Match the following, where [.] greatest integer functionA∫−11[x+[x+[x]]]dxP–6B2∫25([x]+[−x])dxQ1/5C∫0π/4(tan6(x−[x])+tan4(x−[x]))dxR–3D∫−13sgn(x−[x])dxS4 T–4

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Match the following, where $[.]$ greatest integer function
A
$\int_{- 1}^{1} [x + [x + [x]]] d x$
P
–6
B
$2 \int_{2}^{5} ([x] + [- x]) d x$
Q
1/5
C
$\int_{0}^{π / 4} (\tan^{6} (x - [x]) + \tan^{4} (x - [x])) d x$
R
–3
D
$\int_{- 1}^{3} sgn (x - [x]) d x$
S
4

T
–4